Algebraic Expressions - Solutions

 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 z$z$ from y.$y.$
2. One-half of the sum of numbers x$x$ and y.$y.$
3. The number z$z$ multiplied by itself.
4. One-fourth of the product of numbers p$p$ and q.$q.$
5. Numbers x$x$ and y$y$ both squared and added.
6. Number 5 added to three times the product of m$m$ and n.$n.$
7. Product of numbers y$y$ and z$z$ subtracted from 10.
8. Sum of numbers a$a$ and b$b$ subtracted from their product.

Answer: (i) y−z$y-z$

(ii) x+y2$\frac{x+y}{2}$

(iii) z2$z^2$

(iv) pq4$\frac{pq}{4}$

(v) x2+y2$x^2+y^2$

(vi) 3mn+5$3mn+5$

(vii) 10−yz$10-yz$

(viii) ab−(a+b)$ab-\left(a+b\right)$

---

Question 2.(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:

(a) x−3$x-3$

(b) 1+x+x2$1+x+x^2$

(c) y−y3$y-y^3$

(d) 5xy2+7x2y$5x{y}^2+7x^{2}y$

(e) −ab+2b2−3a2$-ab+2b^2-3a^2$

(ii) Identify the terms and factors in the expressions given below:

(a) −4x+5$-4x+5$

(b) −4x+5y$-4x+5y$

(c) 5y+3y2$5y+3y^2$

(d) xy+2x2y2$xy+2x^2{y}^2$

(e) pq+q$pq+q$

(f) 1.2ab−2.4b+3.6a$1.2ab-2.4b+3.6a$

(g) 34x+14$\frac{3}{4}x+\frac{1}{4}$

(h) 0.1p2+0.2q2$0.1p^2+0.2q^2$

Answer: (i) (a) x−3$x-3$

(b) 1+x+x2$1+x+x^2$

Expression

(c) y−y3$y-y^3$

Expression

(d) 5xy2+7x2y$5x{y}^2+7x^{2}y$

Expression

(e) −ab+2b2−3a2$-ab+2b^2-3a^2$

Expression

(ii) (a) −4x+5$-4x+5$

Terms: −4x,5$-4x,5$

Factors: −4,x ; 5$-4,x;5$

(b) −4x+5y$-4x+5y$

Terms: −4x,5y$-4x,5y$

Factors: −4,x ; 5,y$-4,x;5,y$

(c) 5y+3y2$5y+3y^2$

Terms: 5y,3y2$5y,3y^2$

Factors: 5,y ; 3,y,y$5,y;3,y,y$

(d) xy+2x2y2$xy+2x^2{y}^2$

Terms: xy,2x2y2$xy,2x^2{y}^2$

Factors: x,y ; 2x,x,y,y$x,y;2x,x,y,y$

(e) pq+q$pq+q$

Terms: pq,q$pq,q$

Factors: p,q ; q$p,q;q$

(f) 1.2ab−2.4b+3.6a$1.2ab-2.4b+3.6a$

Terms: 1.2ab,−2.4b,3.6a$1.2ab,-2.4b,3.6a$

Factors: 1.2,a,b ; −2.4,b ; 3.6,a$1.2,a,b;-2.4,b;3.6,a$

(g) 34x+14$\frac{3}{4}x+\frac{1}{4}$

Terms: 34x,14$\frac{3}{4}x,\frac{1}{4}$

Factors: 34,x ; 14$\frac{3}{4},x;\frac{1}{4}$

(h) 0.1p2+0.2q2$0.1p^2+0.2q^2$

Terms: 0.1p2,0.2q2$0.1p^2,0.2q^2$

Factors: 0.1,p,p ; 0.2,q,q$0.1,p,p;0.2,q,q$

---

Question 3.Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i)5−3t2$5-3t^2$

(ii)1+t+t2+t3$1+t+t^2+t^3$

(iii)x+2xy+3y$x+2xy+3y$

(iv) 100m+1000n$100m+1000n$

(v)−p2q2+7pq$-p^2{q}^2+7pq$

(vi) 1.2a+0.8b$1.2a+0.8b$

(vii) 3.14r2$3.14r^2$

(viii) 2(l+b)$2\left(l+b\right)$

(ix)  0.1y+0.01y2$0.1y+0.01y^2$

Answer:

S.No.	Expression	Terms	Numerical Coefficient
(i)	5−3t2$5-3t^2$	−3t2$-3t^2$	−3$-3$
(ii)	1+t+t2+t3$1+t+t^2+t^3$	t$t$	1
		t2$t^2$	1
		t3$t^3$	1
(iii)	x+2xy+3y$x+2xy+3y$	x$x$	1
		2xy$2xy$	2
		3y$3y$	3
(iv)	100m+1000n$100m+1000n$	100m$100m$	100
		1000n$1000n$	1000
(v)	−p2q2+7pq$-p^2{q}^2+7pq$	−p2q2$-p^2{q}^2$	−1$-1$
		7pq$7pq$	7
(vi)	1.2a+0.8b$1.2a+0.8b$	1.2a$1.2a$	1.2
		0.8b$0.8b$	0.8
(vii)	3.14r2$3.14r^2$	3.14r2$3.14r^2$	3.14
(viii)	2(l+b)=2l+2b$2\left(l+b\right)=2l+2b$	2l$2l$	2
		2b$2b$	2
(ix)	0.1y+0.01y2$0.1y+0.01y^2$	0.1y$0.1y$	0.1
		0.01y2$0.01y^2$	0.01

---

Question 4.(a) Identify terms which contain x$x$ and give the coefficient of x.$x.$

(i) y2x+y$y^{2}x+y$

(ii) 13y2−8yx$13y^2-8yx$

(iii) x+y+2$x+y+2$

(iv) 5+z+zx$5+z+zx$

(v) 1+x+xy$1+x+xy$

(vi) 12xy2+25$12x{y}^2+25$

(vii) 7x+xy2$7x+x{y}^2$

(b) Identify terms which contain y2$y^2$ and give the coefficient of y2.$y^2.$

(i) 8−xy2$8-x{y}^2$

(ii) 5y2+7x$5y^2+7x$

(iii) 2x2y−15xy2+7y2$2x^{2}y-15x{y}^2+7y^2$

Answer: (a)

S.No.	Expression	Term with factor x$x$	Coefficient of x$x$
(i)	y2x+y$y^{2}x+y$	y2x$y^{2}x$	y2$y^2$
(ii)	13y2−8yx$13y^2-8yx$	−8yx$-8yx$	−8y$-8y$
(iii)	x+y+2$x+y+2$	x$x$	1
(iv)	5+z+zx$5+z+zx$	zx$zx$	z$z$
(v)	1+x+xy$1+x+xy$	x$x$	1
		xy$xy$	y$y$
(vi)	12xy2+25$12x{y}^2+25$	12xy2$12x{y}^2$	12y2$12y^2$
(vii)	7x+xy2$7x+x{y}^2$	xy2$x{y}^2$	y2$y^2$
		7x$7x$	7

(b)

S.No.	Expression	Term contains y2$y^2$	Coefficient of y2$y^2$
(i)	8−xy2$8-x{y}^2$	−xy2$-x{y}^2$	−x$-x$
(ii)	5y2+7x$5y^2+7x$	5y2$5y^2$	5
(iii)	2x2y−15xy2+7y2$2x^{2}y-15x{y}^2+7y^2$	−15xy2$-15x{y}^2$	−15x$-15x$
		7y2$7y^2$	7

---

Question 5.Classify into monomials, binomials and trinomials:

(i) 4y−7x$4y-7x$

(ii) y2$y^2$

(iii) x+y−xy$x+y-xy$

(iv) 100$100$

(v) ab−a−b$ab-a-b$

(vi) 5−3t$5-3t$

(vii) 4p2q−4pq2$4p^{2}q-4p{q}^2$

(viii) 7mn$7mn$

(ix) z2−3z+8$z^2-3z+8$

(x) a2+b2$a^2+b^2$

(xi) z2+z$z^2+z$

(xii) 1+x+x2$1+x+x^2$

Answer:

S.No.	Expression	Type of Polynomial
(i)	4y−7z$4y-7z$	Binomial
(ii)	y2$y^2$	Monomial
(iii)	x+y−xy$x+y-xy$	Trinomial
(iv)	100	Monomial
(v)	ab−a−b$ab-a-b$	Trinomial
(vi)	5−3t$5-3t$	Binomial
(vii)	4p2q−4pq2$4p^{2}q-4p{q}^2$	Binomial
(viii)	7mn$7mn$	Monomial
(ix)	z2−3z+8$z^2-3z+8$	Trinomial
(x)	a2+b2$a^2+b^2$	Binomial
(xi)	z2+z$z^2+z$	Binomial
(xii)	1+x+x2$1+x+x^2$	Trinomial

---

Question 6. State whether a given pair of terms is of like or unlike terms:

(i) 1, 100$1,100$
(ii) −7x,52x$-7x,\frac{5}{2}x$
(iii) −29x,−29y$-29x,-29y$
(iv)  14xy,42yx$14xy,42yx$
(v)  4m2p,4mp2$4m^{2}p,4m{p}^2$
(vi) 12xz,12x2z2$12xz,12x^2{z}^2$

Answer:

S.No.	Pair of terms	Like / Unlike terms
(i)	1, 100	Like terms
(ii)	−7x,52x$-7x,\frac{5}{2}x$	Like terms
(iii)	−29x,−29y$-29x,-29y$	Unlike terms
(iv)	14xy,42yx$14xy,42yx$	Like terms
(v)	4m2p,4mp2$4m^{2}p,4m{p}^2$	Unlike terms
(vi)	12xz,12x2z2$12xz,12x^2{z}^2$	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

Answer: (a) Like terms are:
(i) −xy2,2xy2$-x{y}^2,2x{y}^2$
(ii) −4yx2,20x2y$-4y{x}^2,20x^{2}y$
(iii) 8x2,−11x2,−6x2$8x^2,-11x^2,-6x^2$
(iv) 7y,y$7y,y$
(v) −100x,3x$-100x,3x$
(vi) −11yx,2xy$-11yx,2xy$

(b) Like terms are:
(i) 10pq,−7pq,78pq$10pq,-7pq,78pq$
(ii) 7p,2405p$7p,2405p$
(iii) 8q,−100q$8q,-100q$
(iv) −p2q2,12p2q2$-p^2{q}^2,12p^2{q}^2$
(v) −12,41$-12,41$
(vi) −5p2,701p2$-5p^2,701p^2$
(vii) 13p2q,qp2