NCERT Solutions for Class 7 Maths Chapter 12 (EX 12.1)
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Access NCERT Solutions for Maths Class 7 Chapter 12 – Algebraic Expressions
Exercise 12.1
Refer to page 1-22 for Exercise 12.1 in the PDF
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 \[12{p^2}{q^2}\]
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1
Opting for the NCERT solutions for Ex 12.1 Class 7 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 12.1 Class 7 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
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