### Algebraic Expressions - Solutions 1

CBSE Class –VII Mathematics
NCERT Solutions
Algebraic Expressions (Ex. 12.1)

Question 1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
1. Subtraction of {tex}z{/tex} from {tex}y.{/tex}
2. One-half of the sum of numbers {tex}x{/tex} and {tex}y.{/tex}
3. The number {tex}z{/tex} multiplied by itself.
4. One-fourth of the product of numbers {tex}p{/tex} and {tex}q.{/tex}
5. Numbers {tex}x{/tex} and {tex}y{/tex} both squared and added.
6. Number 5 added to three times the product of {tex}m{/tex} and {tex}n.{/tex}
7. Product of numbers {tex}y{/tex} and {tex}z{/tex} subtracted from 10.
8. Sum of numbers {tex}a{/tex} and {tex}b{/tex} subtracted from their product.
(ii) {tex}\frac{{x + y}}{2}{/tex}
(iii) {tex}{z^2}{/tex}
(iv) {tex}\frac{{pq}}{4}{/tex}
(v) {tex}{x^2} + {y^2}{/tex}
(vi) {tex}3mn + 5{/tex}
(vii) {tex}10 - yz{/tex}
(viii) {tex}ab - \left( {a + b} \right){/tex}

Question 2.(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) {tex}x - 3{/tex}
(b) {tex}1 + x + {x^2}{/tex}
(c) {tex}y - {y^3}{/tex}
(d) {tex}5x{y^2} + 7{x^2}y{/tex}
(e) {tex} - ab + 2{b^2} - 3{a^2}{/tex}
(ii) Identify the terms and factors in the expressions given below:
(a) {tex} - 4x + 5{/tex}
(b) {tex} - 4x + 5y{/tex}
(c) {tex}5y + 3{y^2}{/tex}
(d) {tex}xy + 2{x^2}{y^2}{/tex}
(e) {tex}pq + q{/tex}
(f) {tex}1.2ab - 2.4b + 3.6a{/tex}
(g) {tex}\frac{3}{4}x + \frac{1}{4}{/tex}
(h) {tex}0.1{p^2} + 0.2{q^2}{/tex}
Answer: (i) (a) {tex}x - 3{/tex}
(b) {tex}1 + x + {x^2}{/tex}
Expression
(c) {tex}y - {y^3}{/tex}
Expression
(d) {tex}5x{y^2} + 7{x^2}y{/tex}
Expression

(e) {tex} - ab + 2{b^2} - 3{a^2}{/tex}
Expression
(ii) (a) {tex} - 4x + 5{/tex}
Terms: {tex} - 4x,5{/tex}
Factors: {tex} - 4,x{\text{ }};{\text{ }}5{/tex}
(b) {tex} - 4x + 5y{/tex}
Terms: {tex} - 4x,5y{/tex}
Factors: {tex} - 4,x{\text{ }};{\text{ }}5,y{/tex}
(c) {tex}5y + 3{y^2}{/tex}
Terms: {tex}5y,3{y^2}{/tex}
Factors: {tex}5,y{\text{ }};{\text{ }}3,y,y{/tex}
(d) {tex}xy + 2{x^2}{y^2}{/tex}
Terms: {tex}xy,2{x^2}{y^2}{/tex}
Factors: {tex}x,y{\text{ }};{\text{ }}2x,x,y,y{/tex}
(e) {tex}pq + q{/tex}
Terms: {tex}pq,q{/tex}
Factors: {tex}p,q{\text{ }};{\text{ }}q{/tex}
(f) {tex}1.2ab - 2.4b + 3.6a{/tex}
Terms: {tex}1.2ab, - 2.4b,3.6a{/tex}
Factors: {tex}1.2,a,b{\text{ }};{\text{ }} - 2.4,b{\text{ }};{\text{ }}3.6,a{/tex}
(g) {tex}\frac{3}{4}x + \frac{1}{4}{/tex}
Terms: {tex}\frac{3}{4}x,\frac{1}{4}{/tex}
Factors: {tex}\frac{3}{4},x{\text{ }};{\text{ }}\frac{1}{4}{/tex}
(h) {tex}0.1{p^2} + 0.2{q^2}{/tex}
Terms: {tex}0.1{p^2},0.2{q^2}{/tex}
Factors: {tex}0.1,p,p{\text{ }};{\text{ }}0.2,q,q{/tex}

Question 3.Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i){tex}5 - 3{t^2}{/tex}
(ii){tex}1 + t + {t^2} + {t^3}{/tex}
(iii){tex}x + 2xy + 3y{/tex}
(iv) {tex}100m + 1000n{/tex}
(v){tex} - {p^2}{q^2} + 7pq{/tex}
(vi) {tex}1.2a + 0.8b{/tex}
(vii) {tex}3.14{r^2}{/tex}
(viii) {tex}2\left( {l + b} \right){/tex}
(ix)  {tex}0.1y + 0.01{y^2}{/tex}
 S.No. Expression Terms Numerical Coefficient (i) {tex}5 - 3{t^2}{/tex} {tex} - 3{t^2}{/tex} {tex} - 3{/tex} (ii) {tex}1 + t + {t^2} + {t^3}{/tex} {tex}t{/tex} 1 {tex}{t^2}{/tex} 1 {tex}{t^3}{/tex} 1 (iii) {tex}x + 2xy + 3y{/tex} {tex}x{/tex} 1 {tex}2xy{/tex} 2 {tex}3y{/tex} 3 (iv) {tex}100m + 1000n{/tex} {tex}100m{/tex} 100 {tex}1000n{/tex} 1000 (v) {tex} - {p^2}{q^2} + 7pq{/tex} {tex} - {p^2}{q^2}{/tex} {tex} - 1{/tex} {tex}7pq{/tex} 7 (vi) {tex}1.2a + 0.8b{/tex} {tex}1.2a{/tex} 1.2 {tex}0.8b{/tex} 0.8 (vii) {tex}3.14{r^2}{/tex} {tex}3.14{r^2}{/tex} 3.14 (viii) {tex}2\left( {l + b} \right) = 2l + 2b{/tex} {tex}2l{/tex} 2 {tex}2b{/tex} 2 (ix) {tex}0.1y + 0.01{y^2}{/tex} {tex}0.1y{/tex} 0.1 {tex}0.01{y^2}{/tex} 0.01

Question 4.(a) Identify terms which contain {tex}x{/tex} and give the coefficient of {tex}x.{/tex}
(i) {tex}{y^2}x + y{/tex}
(ii) {tex}13{y^2} - 8yx{/tex}
(iii) {tex}x + y + 2{/tex}
(iv) {tex}5 + z + zx{/tex}
(v) {tex}1 + x + xy{/tex}
(vi) {tex}12x{y^2} + 25{/tex}
(vii) {tex}7x + x{y^2}{/tex}
(b) Identify terms which contain {tex}{y^2}{/tex} and give the coefficient of {tex}{y^2}.{/tex}
(i) {tex}8 - x{y^2}{/tex}
(ii) {tex}5{y^2} + 7x{/tex}
(iii) {tex}2{x^2}y - 15x{y^2} + 7{y^2}{/tex}
 S.No. Expression Term with factor {tex}x{/tex} Coefficient of {tex}x{/tex} (i) {tex}{y^2}x + y{/tex} {tex}{y^2}x{/tex} {tex}{y^2}{/tex} (ii) {tex}13{y^2} - 8yx{/tex} {tex} - 8yx{/tex} {tex} - 8y{/tex} (iii) {tex}x + y + 2{/tex} {tex}x{/tex} 1 (iv) {tex}5 + z + zx{/tex} {tex}zx{/tex} {tex}z{/tex} (v) {tex}1 + x + xy{/tex} {tex}x{/tex} 1 {tex}xy{/tex} {tex}y{/tex} (vi) {tex}12x{y^2} + 25{/tex} {tex}12x{y^2}{/tex} {tex}12{y^2}{/tex} (vii) {tex}7x + x{y^2}{/tex} {tex}x{y^2}{/tex} {tex}{y^2}{/tex} {tex}7x{/tex} 7
(b)
 S.No. Expression Term contains {tex}{y^2}{/tex} Coefficient of {tex}{y^2}{/tex} (i) {tex}8 - x{y^2}{/tex} {tex} - x{y^2}{/tex} {tex} - x{/tex} (ii) {tex}5{y^2} + 7x{/tex} {tex}5{y^2}{/tex} 5 (iii) {tex}2{x^2}y - 15x{y^2} + 7{y^2}{/tex} {tex} - 15x{y^2}{/tex} {tex} - 15x{/tex} {tex}7{y^2}{/tex} 7

Question 5.Classify into monomials, binomials and trinomials:
(i) {tex}4y - 7x{/tex}
(ii) {tex}{y^2}{/tex}
(iii) {tex}x + y - xy{/tex}
(iv) {tex}100{/tex}
(v) {tex}ab - a - b{/tex}
(vi) {tex}5 - 3t{/tex}
(vii) {tex}4{p^2}q - 4p{q^2}{/tex}
(viii) {tex}7mn{/tex}
(ix) {tex}{z^2} - 3z + 8{/tex}
(x) {tex}{a^2} + {b^2}{/tex}
(xi) {tex}{z^2} + z{/tex}
(xii) {tex}1 + x + {x^2}{/tex}
 S.No. Expression Type of Polynomial (i) {tex}4y - 7z{/tex} Binomial (ii) {tex}{y^2}{/tex} Monomial (iii) {tex}x + y - xy{/tex} Trinomial (iv) 100 Monomial (v) {tex}ab - a - b{/tex} Trinomial (vi) {tex}5 - 3t{/tex} Binomial (vii) {tex}4{p^2}q - 4p{q^2}{/tex} Binomial (viii) {tex}7mn{/tex} Monomial (ix) {tex}{z^2} - 3z + 8{/tex} Trinomial (x) {tex}{a^2} + {b^2}{/tex} Binomial (xi) {tex}{z^2} + z{/tex} Binomial (xii) {tex}1 + x + {x^2}{/tex} Trinomial

Question 6. State whether a given pair of terms is of like or unlike terms:
(i) {tex}1,{\text{ }}100{/tex}
(ii) {tex} - 7x,\frac{5}{2}x{/tex}
(iii) {tex} - 29x, - 29y{/tex}
(iv)  {tex}14xy,42yx{/tex}
(v)  {tex}4{m^2}p,4m{p^2}{/tex}
(vi) {tex}12xz,12{x^2}{z^2}{/tex}
 S.No. Pair of terms Like / Unlike terms (i) 1, 100 Like terms (ii) {tex} - 7x,\frac{5}{2}x{/tex} Like terms (iii) {tex} - 29x, - 29y{/tex} Unlike terms (iv) {tex}14xy,42yx{/tex} Like terms (v) {tex}4{m^2}p,4m{p^2}{/tex} Unlike terms (vi) {tex}12xz,12{x^2}{z^2}{/tex} Unlike terms

Question 7.Identify like terms in the following:
(a)  - xy2, -4yx2, 8x2, 2xy2, 7y, -11x2 -100x, -11yx, 20x2y, - 6x2, y, 2xy, 3x
(b) 10pq, 7p, 8q, -p2q2, -7qp, -100q, -23, 12q2p2, -5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
(i) {tex} - x{y^2},2x{y^2}{/tex}
(ii) {tex} - 4y{x^2},20{x^2}y{/tex}
(iii) {tex}8{x^2}, - 11{x^2}, - 6{x^2}{/tex}
(iv) {tex}7y,y{/tex}
(v) {tex} - 100x,3x{/tex}
(vi) {tex} - 11yx,2xy{/tex}
(b) Like terms are:
(i) {tex}10pq, - 7pq,78pq{/tex}
(ii) {tex}7p,2405p{/tex}
(iii) {tex}8q, - 100q{/tex}
(iv) {tex} - {p^2}{q^2},12{p^2}{q^2}{/tex}
(v) {tex} - 12,41{/tex}
(vi) {tex} - 5{p^2},701{p^2}{/tex}
(vii) {tex}13{p^2}q,q{p^2}{/tex}