NCERT Solutions for Class 7 Maths Chapter 12: Algebraic Expressions - Exercise 12.1

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 

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 

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 

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 

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 

(b)  The First term is \[y\] and the second term is\[y\]. Operation performed on them is ‘multiplication’, therefore 

(c)  Now, the first term is \[{x^2}\] and the second term is \[{y^2}\]. Operation performed on them is ‘addition’, therefore 

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 

(b)  The first term is \[m + n\] and the second term is \[3\]. Operation performed on them is ‘multiplication’, therefore 

(c)  Now the first term is \[3\left( {m + n} \right)\] and the second term is \[5\]. Operation performed on them is ‘addition’, therefore 

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 

(ii)  The first term is \[y + z\] and the second term is \[10\]. Operation performed on them is ‘multiplication’, therefore 

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 

(ii)  The first term is \[a\] and the second term is \[b\]. Operation performed on them is ‘multiplication’, therefore 

(iii)  Now, the first term is \[a*b = ab\] and the second term is \[a + b\]. Operation performed on them is ‘subtraction’, therefore 

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

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