NCERT Solutions for Maths Class 7 Chapter 10 Exercise 10.1 - FREE PDF Download
In Class 7 Maths Chapter 10 Exercise 10.1 Solutions students are introduced to the fundamental concepts of algebraic expressions. This exercise focuses on understanding what algebraic expressions are, how they are formed, and how to identify their components such as terms, coefficients, and constants. Through various problems, students will learn to write expressions based on given situations, recognise like and unlike terms, and understand the significance of variables in expressions. Students can access the revised Class 7 Maths NCERT Solutions from our page which is prepared so that you can understand it easily.
These solutions are aligned with the updated CBSE Class 7 Maths Syllabus for Class 7, ensuring students are well-prepared for exams. Class 7 Chapter 10 Maths Exercise 10.1 Questions and Answers PDF provides accurate answers to textbook questions and assists in effective exam preparation and better performance.
Glance on NCERT Solutions Maths Chapter 10 Exercise 10.1 Class 7 | Vedantu
NCERT Solutions Maths Class 7 Chapter 10 Exercise 10.1 covers topics such as - How expressions are Formed, Terms Of An Expression, Coefficients, Like and Unlike Terms and Monomial, Binomial, Trinomial, and Polynomial.
Expressions are the building blocks of algebra, just like bricks are the building blocks of a house. They combine numbers, variables (represented by letters), and operations like addition, subtraction, multiplication, and division.
Terms of An Expression are the ingredients that make it up. Each term can be a single number, a variable, or a combination of a number multiplied by a variable (like 3x or -5y).
If a term has a variable multiplied by a number, the number is called the coefficient. It acts like a multiplier, scaling the value of the variable. For example, in 3x, the coefficient is 3.
Like terms are the terms that have the same variables raised to the same power. Imagine them as twins in the expression family! (e.g., 2x and 5x)
Unlike terms, they have different variables or the same variable raised to different powers. (e.g., 2x and 3y,or 2x and x²)
Monomial: One term (e.g., 5, x, -7y²)
Binomial: Two terms (e.g., 2x + 3y, 5 - a)
Trinomial: Three terms (e.g., x² + 2xy - 4, 3a - 2b + 1)
Polynomial: Any expression with more than two terms (e.g., x³ - 2x² + 5x - 1)
Maths Class 7 Chapter 10 Exercise 10.1 covers 7 fully solved questions and solutions.
Access NCERT Solutions for Maths Class 7 Chapter 10 - Algebraic Expressions
Exercise 10.1
1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
(i) Subtraction of \[z\] from \[y\].
Ans: It is given that the first term is \[y\] and the second term is \[z\]. The operation performed on them is ‘subtraction, therefore
1st term | 2nd term | Operation | Expression |
\[y\] | \[z\] | - | \[y - z\] |
Thus the expression is \[y - z\].
(ii) One-half of the sum of numbers \[x\] and \[y\].
Ans: It is given that the first term is \[x\] and the second term is \[y\]. Operation performed on them is ‘addition’ and then ‘one-half of the sum’, therefore
1st term | 2nd term | Operation | Expression |
\[x\] | \[y\] | + | \[x{\text{ + }}y\] |
Term | Operation | Expression |
\[x + y\] | One-half, i.e., \[\dfrac{1}{2}\] | \[\dfrac{1}{2}\left( {a + b} \right)\] |
Thus the expression is \[\dfrac{1}{2}\left( {x + y} \right)\].
(iii) The number \[z\] multiplied by itself.
Ans: It is given that the first term is \[z\] and the second term is \[z\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[z\] | \[z\] | \[*\] | \[z * z = {z^2}\] |
Thus the expression is \[z * z = {z^2}\].
(iv) One-fourth of the product of numbers \[p\] and \[q\].
Ans: It is given that the first term is \[p\] and the second term is \[q\]. Operation performed on them is ‘multiplication’ and then ‘one-fourth of the product’, therefore
1st term | 2nd term | Operation | Expression |
\[p\] | \[q\] | \[*\] | \[p * q = pq\] |
Term | Operation | Expression |
\[pq\] | One-fourth, i.e., \[\dfrac{1}{4}\] | \[\dfrac{1}{4}\left( {pq} \right)\] |
Thus the expression is\[\dfrac{1}{4}\left( {pq} \right)\].
(v) Numbers \[x\] and \[y\] both squared and added.
Ans: (a) The first term is \[x\] and the second term is \[x\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[x\] | \[x\] | \[*\] | \[x * x = {x^2}\] |
(b) The First term is \[y\] and the second term is\[y\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[y\] | \[y\] | \[*\] | \[y * y = {y^2}\] |
(c) Now, the first term is \[{x^2}\] and the second term is \[{y^2}\]. Operation performed on them is ‘addition’, therefore
1st term | 2nd term | Operation | Expression |
\[{x^2}\] | \[{y^2}\] | \[ + \] | \[{x^2} + {y^2}\] |
Thus the expression is \[{x^2} + {y^2}\].
(vi) Number \[5\] added to three times the product of \[m\] and \[n\].
Ans: (a) The first term is \[m\] and the second term is \[n\]. Operation performed on them is ‘addition’, therefore
1st term | 2nd term | Operation | Expression |
\[m\] | \[n\] | \[ + \] | \[m + n\] |
(b) The first term is \[m + n\] and the second term is \[3\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[m + n\] | \[3\] | \[*\] | \[3\left( {m + n} \right)\] |
(c) Now the first term is \[3\left( {m + n} \right)\] and the second term is \[5\]. Operation performed on them is ‘addition’, therefore
1st term | 2nd term | Operation | Expression |
\[3\left( {m + n} \right)\] | \[5\] | \[ + \] | \[3\left( {m + n} \right) + 5\] |
Thus the expression is \[3\left( {m + n} \right) + 5\].
(vii) Product of numbers \[y\] and \[z\] subtracted from \[10\].
Ans: (a) The first term is \[y\] and the second term is \[z\] . Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[y\] | \[z\] | \[*\] | \[y * z = yz\] |
(ii) The first term is \[y + z\] and the second term is \[10\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[10\] | \[y*z = yz\] | \[ - {\text{ }}\] | \[ 10 - yz\] |
Thus the expression is \[ 10 - yz\].
(viii) Sum of numbers \[a\] and \[b\] subtracted from their product.
Ans: (i) The first term is \[a\] and the second term is \[b\] . Operation performed on them is ‘addition’, therefore
1st term | 2nd term | Operation | Expression |
\[a\] | \[b\] | \[ + \] | \[a + b\] |
(ii) The first term is \[a\] and the second term is \[b\]. Operation performed on them is ‘multiplication’, therefore
1st term | 2nd term | Operation | Expression |
\[a\] | \[b\] | \[*\] | \[a*b = ab\] |
(iii) Now, the first term is \[a*b = ab\] and the second term is \[a + b\]. Operation performed on them is ‘subtraction’, therefore
1st term | 2nd term | Operation | Expression |
\[ab\] | \[a + b\] | \[ - \] | \[ab - \left( {a + b} \right)\] |
Thus the expression is \[ab - \left( {a + b} \right)\].
2. (i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) \[x - 3\]
Ans: Tree diagram of \[x - 3\] will be:
(b) \[1 + x + {x^2}\]
Ans: Tree diagram of \[1 + x + {x^2}\] will be:
(c) \[y - {y^3}\]
Ans: Tree diagram of \[y - {y^3}\] will be:
(d) \[5x{y^2} + 7{x^2}y\]
Ans: Tree diagram of \[5x{y^2} + 7{x^2}y\] will be:
(e) \[ - ab + 2{b^2} - 3{a^2}\]
Ans: Tree diagram of \[ - ab + 2{b^2} - 3{a^2}\] will be:
(ii) Identify the terms and factors in the expressions given below:
(a) \[ - 4x + 5\]
Ans: The given expression \[ - 4x + 5\]is achieved when \[ - 4x\] and \[5\] are added, therefore terms of the expression \[ { - 4x + 5} \]are \[ - 4x\] and \[5\].
\[ - 4x\] is achieved by multiplication \[ - 4\] and \[x\]. Therefore, factors of \[ - 4x\] are \[ - 4\] and \[x\].
(b) \[ { - 4x + 5y} \]
Ans: The given expression\[ - 4x + 5y\] is achieved when \[ - 4x\] and \[5y\] are added, therefore terms of the expression \[ - 4x + 5y\] are \[ - 4x\] and \[5y\].
\[ - 4x\] is achieved by multiplication \[ - 4\] and \[x\]. Similarly, \[5y\] is achieved by multiplication \[5\] and \[y\]. Therefore, factors of \[ - 4x\] are \[ - 4\] and \[x\] and of \[5y\] are \[5\] and \[y\].
(c) \[5y + 3{y^2}\]
Ans: Given expression \[5y + 3{y^2}\] is achieved when \[5y\] and \[3{y^2}\] are added, therefore terms of the expression \[5y + 3{y^2}\] are \[5y\] and \[3{y^2}\].
\[5y\] is achieved by multiplication \[5\] and \[y\]. Similarly, \[3{y^2}\] is achieved by multiplication of \[3\], \[y\] and \[y\]. Therefore, factors of \[5y\] are \[5\] and \[y\] and of \[3{y^2}\] are \[3\], \[y\] and \[y\].
(d) \[xy + 2{x^2}{y^2}\]
Ans: Given expression \[xy + 2{x^2}{y^2}\] is achieved when \[xy\] and \[2{x^2}{y^2}\] are added , therefore terms of the expression \[xy + 2{x^2}{y^2}\] are \[xy\] and \[2{x^2}{y^2}\].
\[xy\] is achieved by multiplication \[x\] and \[y\]. Similarly, \[2{x^2}{y^2}\] is achieved by multiplication of \[2\], \[x\], \[x\], \[y\] and \[y\]. Therefore, factors of \[xy\] are \[x\] and \[y\] and of \[2{x^2}{y^2}\] are \[2\], \[x\], \[x\], \[y\] and \[y\].
(e) \[pq + q\]
Ans: The given expression \[pq + q\] is achieved when \[pq\] and \[q\] are added , therefore terms of the expression \[pq + q\] are \[pq\] and \[q\].
\[pq\] is achieved by multiplication\[p\] and \[q\]. Therefore, factors of \[pq\] are \[p\] and \[q\].
(f) \[1.2ab - 2.4b + 3.6a\]
Ans: The given expression \[1.2ab - 2.4b + 3.6a\] is achieved when \[1.2ab\], \[ - 2.4b\] and \[3.6a\] are added , therefore terms of the expression \[1.2ab - 2.4b + 3.6a\] are \[1.2ab\], \[ - 2.4b\] and \[3.6a\].
\[1.2ab\] is achieved by multiplication of \[1.2\], \[a\] and \[b\], similarly \[ - 2.4b\] is achieved by multiplication of \[ - 2.4\] and \[b\] and similarly \[3.6a\] is achieved by multiplication of \[3.6\] and \[a\]. Therefore, factors of \[1.2ab\] are \[1.2\], \[a\] and \[b\], factors of \[ - 2.4b\] are \[ - 2.4\] and \[b\] and of \[3.6a\] are \[3.6\] and \[a\].
(g) \[\dfrac{3}{4}x + \dfrac{1}{4}\]
Ans: The given expression \[\dfrac{3}{4}x + \dfrac{1}{4}\] is achieved when \[\dfrac{3}{4}x\] and \[\dfrac{1}{4}\] are added, therefore terms of the expression \[\dfrac{3}{4}x + \dfrac{1}{4}\] are \[\dfrac{3}{4}x\] and \[\dfrac{1}{4}\].
\[\dfrac{3}{4}x\] is achieved by multiplication of \[\dfrac{3}{4}\] and \[x\]. Therefore, factors of \[\dfrac{3}{4}x\] are \[\dfrac{3}{4}\] and \[x\].
(g) \[0.1{p^2} + 0.2{q^2}\]
Ans: The given expression \[0.1{p^2} + 0.2{q^2}\] is achieved when \[0.1{p^2}\] and \[0.2{q^2}\] are added, therefore terms of the expression \[0.1{p^2} + 0.2{q^2}\] are \[0.1{p^2}\] and \[0.2{q^2}\].
\[0.1{p^2}\] is achieved by multiplication of \[0.1\], \[p\] and \[p\]. \[0.2{q^2}\] is achieved by multiplication of \[0.2\], \[q\] and \[q\]. Therefore, factors of \[0.1{p^2}\] are \[0.1\], \[p\] and \[p\] and of \[0.2{q^2}\] are \[0.2\], \[q\] and \[q\].
3. Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) \[5 - 3{t^2}\]
Ans: In the expression \[5 - 3{t^2}\], \[5\] is the constant term and \[ - 3{t^2}\] is the term other than the constant. Coefficient of \[ - 3{t^2}\] is \[ - 3\].
(ii) \[1 + t + {t^2} + {t^3}\]
Ans: In the expression \[1 + t + {t^2} + {t^3}\], \[1\] is the constant term and \[t\], \[{t^2}\] and \[{t^3}\] are the terms other than the constant. Coefficient of \[t\] is \[1\], of \[{t^2}\] is \[1\] and of \[{t^3}\] is \[1\].
(iii) \[x + 2xy + 3y\]
Ans: In the expression \[x + 2xy + 3y\], there is no constant term and \[x\], \[2xy\] and \[3y\] are the terms other than the constant. Coefficient of \[x\] is \[1\], of \[2xy\] is\[2\] and of \[3y\] is \[3\].
(iv) \[100m + 1000n\]
Ans: In the expression \[100m + 1000n\], there is no constant term and \[100m\] and \[1000n\] are the terms other than the constant. Coefficient of \[100m\] is \[100\] and of \[1000n\] is \[1000\].
(v) \[ - {p^2}{q^2} + 7pq\]
Ans: In the expression \[ - {p^2}{q^2} + 7pq\], there is no constant term and \[ - {p^2}{q^2}\] and \[7pq\] are the terms other than the constant. Coefficient of \[ - {p^2}{q^2}\] is \[ - 1\] and of \[7pq\] is \[7\].
(vi) \[1.2a + 0.8b\]
Ans: In the expression \[1.2a + 0.8b\], there is no constant term and \[1.2a\] and \[0.8b\] are the terms other than the constant. Coefficient of \[1.2a\] is \[1.2\] and of \[0.8b\] is \[0.8\].
(vii) \[3.14{r^2}\]
Ans: In the expression \[3.14{r^2}\], there is no constant term and \[3.14{r^2}\] is the term other than the constant. Coefficient of \[3.14{r^2}\] is \[3.14\].
(viii) \[2\left( {l + b} \right) = 2l + 2b\]
Ans: In the expression \[2\left( {l + b} \right) = 2l + 2b\], there is no constant term and \[2l\] and \[2b\] are the terms other than the constant. Coefficient of \[2l\] is \[2\] and of \[2b\] is \[2\].
(ix) \[0.1y + 0.01{y^2}\]
Ans: In the expression \[0.1y + 0.01{y^2}\], there is no constant term and \[0.1y\] and \[0.01{y^2}\] are the terms other than the constant. Coefficient of \[0.1y\] is \[0.1\] and of \[0.01{y^2}\] is \[0.01\].
4. (a) Identify terms which contain \[x\] and give the coefficient of \[x\].
(i) \[{y^2}x + y\].
Ans: In the expression \[{y^2}x + y\], the term which contains \[x\] is \[{y^2}x\]. The coefficient of \[x\] in \[{y^2}x\] is \[{y^2}\].
(ii) \[13{y^2} - 8yx\].
Ans: In the expression \[13{y^2} - 8yx\], the term which contains \[x\] is \[ - 8yx\]. The coefficient of \[x\]in \[ - 8yx\] is \[ - 8y\].
(iii) \[x + y + 2\].
Ans: In the expression \[x + y + 2\], the term which contains \[x\] is \[x\]. The coefficient of \[x\] in \[x\] is \[1\].
(iv) \[5 + z + zx\].
Ans: In the expression \[5 + z + zx\], the term which contains \[x\] is \[zx\]. The coefficient of \[x\] in \[zx\] is \[z\].
(v) \[1 + x + xy\].
Ans: In the expression \[1 + x + xy\], terms which contain \[x\] are \[x\] and \[xy\]. The coefficient of \[x\] in \[x\] is \[1\] and in \[xy\] is\[y\].
(vi) \[12x{y^2} + 25\].
Ans: In the expression \[12x{y^2} + 25\], the term which contains \[x\] is \[12x{y^2}\]. The coefficient of \[x\] in \[12x{y^2}\] is \[12{y^2}\].
(vii) \[7x + x{y^2}\].
Ans: In the expression \[7x + x{y^2}\], terms which contain \[x\] are \[x{y^2}\] and \[7x\]. The coefficient of \[x\] in \[x{y^2}\] is \[{y^2}\] and in \[7x\] is \[7\].
(b) Identify terms which contain \[{y^2}\] and give the coefficient of \[{y^2}\].
(i) \[8 - x{y^2}\]
Ans: In the expression \[8 - x{y^2}\], the term which contains \[{y^2}\] is \[ - x{y^2}\]. The coefficient of \[{y^2}\] in \[ - x{y^2}\] is \[ - x\].
(ii) \[5{y^2} + 7x\]
Ans: In the expression \[5{y^2} + 7x\], the term which contains \[{y^2}\] is \[5{y^2}\]. The coefficient of \[{y^2}\]in \[5{y^2}\] is \[5\].
(iii) \[2{x^2}y - 15x{y^2} + 7{y^2}\]
Ans: In the expression \[2{x^2}y - 15x{y^2} + 7{y^2}\], terms which contain \[{y^2}\] are \[ - 15x{y^2}\] and \[7{y^2}\]. The coefficient of \[{y^2}\] in \[ - 15x{y^2}\] is \[ - 15x\] and in \[7{y^2}\] is \[7\].
5. Classify into monomials, binomials and trinomials:
(i) \[4y - 7x\]
Ans: The expression \[4y - 7x\] consists of two terms, i.e., \[4y\] and \[ - 7x\] . Because \[4y - 7x \] consists of two terms. Therefore, \[4y - 7x\] is a binomial.
(ii) \[{y^2}\]
Ans: The expression \[{y^2}\] consists of one term, i.e., \[{y^2}\]. Because \[{y^2}\] consists of one term. Therefore, \[{y^2}\] is a monomial.
(iii) \[x + y - xy\]
Ans: The expression \[x + y + xy\], consists of three terms, i.e., \[x\], \[y\] and \[ - xy\]. Because \[x + y + xy\] consists of three terms. Therefore, \[x + y + xy\] is a trinomial.
(iv) \[100\]
Ans: The expression \[100\] consists of one term, i.e., \[100\]. Because \[100\] consists of one term. Therefore, \[100\] is a monomial.
(v) \[ab - a - b\]
Ans: The expression \[ab - a - b\] consists of three terms, i.e., \[ab\], \[ - a\] and \[ - b\]. Because \[ab - a - b\] consists of three terms. Therefore, \[ab - a - b\] is a trinomial.
(vi) \[5 - 3t\]
Ans: The expression \[5 - 3t\] consists of two terms, i.e., \[5\] and \[ - 3t\]. Because \[5 - 3t\] consists of two terms. Therefore, \[5 - 3t\] is a binomial.
(vii) \[4{p^2}q - 4p{q^2}\]
Ans: The expression \[4{p^2}q - 4p{q^2}\] consists of two terms, i.e., \[4{p^2}q\] and \[ - 4p{q^2}\]. Because \[4{p^2}q - 4p{q^2}\] consists of two terms. Therefore, \[4{p^2}q - 4p{q^2}\] is a binomial.
(viii) \[7mn\]
Ans: The expression \[7mn\] consists of one term, i.e., \[7mn\]. Because \[7mn\] consists of one term. Therefore, \[7mn\] is a monomial.
(ix) \[{z^2} - 3z + 8\]
Ans: The expression \[{z^2} - 3z + 8\] consists of three terms, i.e., \[{z^2}\], \[ - 3z\] and \[8\]. Because \[{z^2} - 3z + 8\] consists of three terms. Therefore,\[{z^2} - 3z + 8\] is a trinomial.
(x) \[{a^2} + {b^2}\]
Ans: The expression \[{a^2} + {b^2}\] consists of two terms, i.e., \[{a^2}\] and \[{b^2}\]. Because \[{a^2} + {b^2}\] consists of two terms. Therefore, \[{a^2} + {b^2}\] is a binomial.
(xi) \[{z^2} + z\]
Ans: The expression \[{z^2} + z\] consists of two terms, i.e., \[{z^2}\] and \[z\] . Because \[{z^2} + z\] consists of two terms. Therefore, \[{z^2} + z\] is a binomial.
(xii) \[1 + x + {x^2}\]
Ans: The expression \[1 + x + {x^2}\] consists of three terms, i.e., \[1\], \[x\] and \[{x^2}\]. Because \[1 + x + {x^2}\] consists of three terms. Therefore, \[1 + x + {x^2}\] is a trinomial.
6. State whether a given pair of terms is of like or unlike terms:
(i) \[1,{\text{ }}100\]
Ans: Factor of \[1\] is \[1\].
Factor of \[100\] is \[100\].
Algebraic factor \[1\] and \[100\] is none, i.e., and have the same algebraic factor. Therefore, \[1\] and \[100\] are like terms.
(ii) \[ - 7x,{\text{ }}\dfrac{5}{2}x\]
Ans: Factors of \[ - 7x\] are \[ - 7\] and \[x\].
Factors of \[\dfrac{5}{2}x\] are \[\dfrac{5}{2}\] and \[x\] .
Algebraic factor of \[ - 7x\] is \[x\] and of \[\dfrac{5}{2}x\] is \[x\]. Because \[ - 7x\] and \[\dfrac{5}{2}x\] have the same algebraic factor. Therefore, \[ - 7x\] and \[\dfrac{5}{2}x\] are like terms.
(iii) \[ - 29x,{\text{ }} - 29y\]
Ans: Factors of \[ - 29x\] are \[ - 29\] and \[x\].
Factors of \[ - 29y\] are \[ - 29\] and \[y\].
Algebraic factor of \[ - 29x\] is \[x\] and of \[ - 29y\] is \[y\]. Because \[ - 29x\] and \[ - 29y\] do not have the same algebraic factor. Therefore, \[ - 29x\] and \[ - 29y\] are unlike terms.
(iv) \[14xy,{\text{ }}42yx\]
Ans: Factors of \[14xy\] are \[14\], \[x\] and \[y\].
Factors of \[42yx\] are \[42\], \[y\] and \[x\].
Algebraic factors of \[14xy\] are \[x\] and \[y\] and of \[42yx\] are \[y\] and \[x\]. Because \[14xy\] and \[42yx\] have the same algebraic factor, i.e., \[x\] and \[y\]. Therefore, \[14xy\] and \[42yx\] are like terms.
(v) \[4{m^2}p,{\text{ }}4m{p^2}\]
Ans: Factors of \[4{m^2}p\] are \[4\], \[m\], \[m\] and \[p\].
Factors of \[4m{p^2}\] are \[4\], \[m\], \[p\] and \[p\].
Algebraic factors of \[4{m^2}p\] are \[m\], \[m\] and \[p\] and of \[4m{p^2}\] are \[m\], \[p\] and \[p\]. Because \[4{m^2}p\] and \[4m{p^2}\] have different algebraic factors. Therefore, \[4{m^2}p\] and \[4m{p^2}\] are unlike terms.
(vi) \[12xz,{\text{ }}12{x^2}{z^2}\]
Ans: Factors of \[12xz\] are \[12\], \[x\] and \[z\].
Factors of \[12{x^2}{z^2}\] are \[12\], \[x\], \[x\], \[z\] and \[z\].
Algebraic factors of \[12xz\] are \[x\] and \[z\] and of \[12{x^2}{z^2}\] are \[x\], \[x\], \[z\] and \[z\]. Because \[12xz\] and \[12{x^2}{z^2}\] have different algebraic factors. Therefore, \[12xz\] and \[12{x^2}{z^2}\] are unlike terms.
7. Identify like terms in the following:
(a) \[ - x{y^2}, - 4y{x^2},8{x^2},2x{y^2},7y, - 11{x^2}, - 100x, - 11yx,20{x^2}y, - 6{x^2},y,2xy,3x\]
Ans: Factors of \[ - x{y^2}\] are\[ - 1\], \[x\], \[y\] and \[y\]. Algebraic factors of \[ - x{y^2}\] are \[x\], \[y\] and \[y\].
Factors of \[ - 4y{x^2}\] are \[ - 4\], \[y\], \[x\] and \[x\]. Algebraic factors of \[ - 4y{x^2}\] are \[y\], \[x\] and \[x\].
Factors of \[8{x^2}\] are \[8\], \[x\], and \[x\]. Algebraic factors of \[8{x^2}\] are \[x\] and \[x\].
Factors of \[2xy\] are \[2\], \[x\] and \[y\]. Algebraic factors of \[2xy\] are \[x\] and \[y\].
Factors of \[7y\] are \[7\] and \[y\]. Algebraic factor of \[7y\] is \[y\].
Factors of \[ - 11{x^2}\] are \[ - 11\], \[x\] and \[x\]. Algebraic factors of \[ - 11{x^2}\] are \[ - 11\], \[x\] and \[x\].
Factors of \[ - 100x\] are \[ - 100\] and \[x\]. Algebraic factor of \[ - 100x\] is \[x\].
Factors of \[ - 11yx\] are \[ - 11\], \[x\] and \[y\]. Algebraic factors of \[ - 11yx\] are \[x\] and \[y\].
Factors of \[20{x^2}y\] are \[20\], \[x\], \[x\] and \[y\]. Algebraic factors of \[20{x^2}y\] are \[x\], \[x\] and \[y\].
Factors of \[ - 6{x^2}\] are \[ - 6\], \[x\] and \[x\]. Algebraic factors of \[ - 6{x^2}\] are \[x\] and \[x\].
Factor of \[y\] is \[y\]. Algebraic factor of \[y\] is \[y\].
Factors of \[2xy\] are \[2\], \[x\] and \[y\]. Algebraic factors of \[2xy\] are \[x\] and \[y\].
Factors of \[3x\] are \[3\] and \[x\]. Algebraic factor of \[3x\] is \[x\].
One can observe that the following pairs have same algebraic variable, i.e., they are like terms:
\[ - x{y^2} \] and \[ 2x{y^2} \]
\[ - 4y{x^2}\] and \[20{x^2}y\]
\[y\] and \[7y\]
\[ - 100x\] and \[3x\]
\[ - 11yx\] and \[2xy\]
\[8{x^2}\], \[ - 6{x^2}\] and \[ - 11{x^2}\]
(b) \[10pq,7p,8q, - {p^2}{q^2}, - 7pq, - 100q, - 23,12{q^2}{p^2}, - 5{p^2},41,2405p,78pq,13{p^2}q,q{p^2},701{p^2}\]
Ans: Factors of \[10pq\] are \[p\], \[10\] and \[q\]. Algebraic factors of \[10pq\] are \[p\] and \[q\].
Factors of \[7p\] are \[7\] and \[p\]. Algebraic factor of \[7p\] is \[p\].
Factors of \[8q\] are \[8\] and \[q\]. Algebraic factor of \[8q\] is \[q\].
Factors of \[ - {p^2}{q^2}\] are \[ - 1\], \[p\],\[p\] , \[q\] and \[q\]. Algebraic factors of \[ - {p^2}{q^2}\] are \[p\], \[p\], \[q\] and \[q\].
Factors of \[ - 7pq\] are \[ - 7\] , \[q\] and \[p\]. Algebraic factors of \[ - 7pq\]are \[q\] and \[p\].
Factors of \[ - 100q\] are \[ - 100\] and \[q\]. Algebraic factor of \[ - 100q\] is \[q\].
Factor of \[ - 23\] is \[ - 23\]. Algebraic factor of \[ - 23\] is none.
Factors of \[12{p^2}{q^2}\] are \[12\] , \[q\], \[q\], \[p\] and \[p\]. Algebraic factors of \[12{p^2}{q^2}\] are \[q\], \[q\], \[p\]and \[p\].
Factors of \[ - 5{p^2}\] are \[ - 5\], \[p\] and \[p\]. Algebraic factors of \[ - 5{p^2}\] are \[p\] and \[p\].
Factor of \[41\] is \[41\]. Algebraic factor of \[41\] is\[41\].
Factors of \[2405p\] are \[2405\] and \[p\]. Algebraic factor of \[2405p\] is \[p\].
Factors of \[78pq \] are \[78\] , \[p\] and \[q\]. Algebraic factors of \[78pq\]are \[p\] and \[q\].
Factors of \[13{p^2}q\] are \[13\],\[p\],\[p\] and \[q\]. Algebraic factors of \[13{p^2}q\] is \[p\],\[p\] and \[q\].
Factors of \[q{p^2}\] are \[p\], \[p\] and \[q\]. Algebraic factors of \[q{p^2}\] are \[p\], \[p\] and \[q\].
Factors of \[701{p^2}\] are \[701\], \[p\] and \[p\]. Algebraic factors of \[701{p^2}\] are \[p\] and \[p\].
One can observe that the following pairs have same algebraic variable, i.e., they are like terms:
\[ - 7pq\], \[78pq\] and \[10pq\]
\[2405p\] and \[7p\]
\[ - 100q\] and \[8q\]
\[41\] and \[ - 23 \]
\[701{p^2}\] and \[ - 5{p^2}\]
\[q{p^2}\] and \[13{p^2}q\]
\[ - {p^2}{q^2}\] and \[12{p^2}{q^2}\]
Conclusion
Class 7 Maths Chapter 10 Exercise 10.1 Solutions Algebraic Expressions has laid a strong foundation for understanding the basics of algebra. Through Class 7 Chapter 10 Maths Exercise 10.1, students have learned to identify and construct algebraic expressions, recognize terms, coefficients, and constants, and differentiate between like and unlike terms. Understanding these fundamental concepts is essential for progressing in algebra and developing problem-solving skills. By practising these problems, students are well-prepared to tackle more complex algebraic operations in future exercises.
Class 7 Maths Chapter 10: Exercises Breakdown
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CBSE Class 7 Maths Chapter 10 Other Study Materials
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Chapter-Specific NCERT Solutions for Class 7 Maths
Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
S.No. | NCERT Solutions Class 7 Maths Chapter-wise PDF |
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FAQs on NCERT Solutions for Class 7 Maths Chapter 10 - Algebraic Expressions Exercise 10.1
1. What is an algebraic expression and its types we studied in Class 7 Maths Chapter 10 Exercise 10.1 Solutions Algebraic Expressions.
An algebraic expression is a mathematical phrase that includes variables, constants, and operators. Types include monomials (single term), binomials (two terms), and polynomials (multiple terms).
2. How do you simplify algebraic expressions in class 7 maths chapter 10 algebraic expressions exercise 10.1 solutions?
Simplifying algebraic expressions involves combining like terms, performing arithmetic operations, and reducing the expression to its simplest form.
3. What are the basic rules of algebra in Class 7 Chapter 10 Maths Exercise 10.1?
Basic rules include the commutative, associative, and distributive properties, as well as rules for combining like terms and performing operations with variables and constants.
4. How do you write algebraic expressions from word problems?
As we studied in Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1 solutions, To write algebraic expressions from word problems, identify the variables and constants, translate the words into mathematical symbols, and form the expression using arithmetic operations.
5. What is the difference between an equation and an expression in NCERT Solutions for Class 7 Maths Chapter 10 Ex 10.1?
An equation is a mathematical statement that asserts the equality of two expressions, while an expression is a combination of variables, constants, and operations without an equality sign.
6. What is a coefficient in an algebraic expression?
A coefficient is a numerical factor that multiplies a variable in a term. For example, in 5x5x, 5 is the coefficient. Learn more about coefficients in NCERT Solutions for Class 7 Maths Chapter 10 Ex 10.1.
7. What is a constant in an algebraic expression?
A constant is a fixed numerical value in an expression that does not change. For example, in the expression 4+3x4+3x, 4 is the constant.
8. How do you identify like and unlike terms you studied in class 7 maths chapter 10 algebraic expressions ex 10.1?
Like terms have the same variable raised to the same power, while unlike terms have different variables or powers. For example, 3x and 5x are like terms, but 3x and 3y are unlike terms. Understand this topic more efficiently from NCERT Class 7 Maths Chapter 10 Exercise 10.1.
9. How can I form an algebraic expression from a given statement answer this according to class 7 maths chapter 10 algebraic expressions ex 10.1.
To form an algebraic expression, translate the words into mathematical symbols, identify the variables and constants, and write them as an expression using arithmetic operations.
10. What is the significance of learning algebraic expressions from NCERT Class 7 Maths Chapter 10 Exercise 10.1?
Learning algebraic expressions is crucial as they form the basis for understanding higher-level algebra and solving equations, which are used in various real-life applications.