NCERT Solutions for Class 7 Maths Chapter 10 - Algebraic Expressions Exercise 10.1

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 

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 \[12{p^2}{q^2}\]

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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