NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.

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

Question 1.
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of z from y.
(ii) One-half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
Answer:
(i) y – z
(ii) \(\frac { 1 }{ 2 }\)(x + y)
(iii) z²
(iv) \(\frac { 1 }{ 4 }\)pq
(v) x² + y²
(vi) 5 + 3mn
(vii) 10 – yz
(viii) ab – (a + b)

Question 2.
(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x²
(c) y – y³
(d) 5xy² + 7x²y
(e) – ab + 2b² – 3a²

(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2ab- 2.4 b + 3.6a
(g) \(\frac { 3 }{ 4 }\)x + \(\frac { 1 }{ 4 }\)
(h) 0.1p² + 0.2p²
Answer:
(i) (a) x – 3
Terms : x; – 3 Factors x; -3
1 + x + x²

(b) 1 + x + x²
Terms = 1; x; x²
Factors = 1; x; x, x (x² )

(d) 5xy² + 7x² y
Terms: 5xy²; 7x² y
Factors: 5, x, y, y; 7, x, x, y

(e) -ab + 2b² – 3a²
Terms: -ab; 2b², -3a²
Factors: -1, a, b; 2; b; b; 3, a, a

(ii)

Expression	Terms	Factors
(a) -4x + 5	-4x 5	-4x and z 5 and y
(b) – 4x + 5y	-4x 5y	– 4 and z 5 and y
(c) 5y + 3y²	5y 3y²	5 and y 3, y and y
(d) xy + 2x² y²	Xy 2x²y²	x and y 2, x.x, y and y
(e) pq + q	Pq q	p and q q
(f) 1.2ab – 2.4 b + 3.6a	1.2ab – 2.4 b 3.6a	1.2, a and b. -2.4 and b 3.6 and a
(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\)	\(\frac{3}{4}\)x \(\frac{1}{4}\)	\(\frac{3}{4}\) and x \(\frac{1}{4}\)
(h) 0.lp² + 0.2q²	0.1p² 0.2q²	0.1, p,p 0.2, q and q

Question 3.
Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t²
(ii) 1 + t + t² + t³
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) -p²q² + 7pq
(vi) 1.2a + 0.8b
(vii) 3.14r²
(viii) 2(l + b)
(ix) 0.1y + 0.01y²
Answer:

Expression	Terms (other than constant)	Numerical coefficient
(i) 5 – 3t²	– 3t²	-3
(ii) 1 + t + t² + t³	t t²t³	1 1 1
(iii) x + 2xy + 3y	x 2xy 3y	1 2 3
(iv) 100 m + lOOOn	100m 1000n	100 1000
(v) -p²q² + 7pq	-p²q² 7pq	-1 7
(vi) 1.2a + 0.8b	1.2a 0.8b	1.2 0.8
(vii) 3.14r²	3.14r²	3.14
(viii) 2(l + b)	2l 2b	2 2
(ix) 0.1y + 0.01y²	0.1y 0.01y²	0.1 0.01

Question 4.
(a) Identify terms which contain x and give the coefficient of x.
(i) y²x + y
(ii) 13y² – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(iv) 1+x + xy
(vi) 12xy² + 25
(vii) 7x + xy²

(b) Identify terms which contain y² and give the coefficient of y².
(i) 8-xy²
(ii) 5y² + 7x
(iii) 2x²y – 15xy² + 7y²
Answer:

Expression	Term containing x	Coefficient of x
(i) y²x + y	y²x	y²
(ii) x + y + 2	– 8yx	– 8y
(iii) 5 + z + zx	x	l
(iv) 5 + z + zx	zx	Z
(v) 1 + x + xy	x xy	1 y
(vi) 12xy²+ 25	12xy²	12y²
(vii) 7x + xy²	7x xy²	7 y²

(b)

Expression	Term containing y²	Coefficient of y²
(i) 8 – xy²	-xy²	-X
(ii) 5y² + 7x	5y²	5
(iii) 2x²y – 15xy² + 7y²	– 15xy²7f	– 15x 7

Question 5.
Classify into monomials, binomials and trinomials.
(i) 4y – 7z
(ii) y²
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p²q – 4pq²
(viii) 7mn
(ix) z² – 3z + 8
(x) a² + b²
(xi) z² + z
(xii) 1 + x + x²
Answer:
(i) 4y – 7z
The expression 4y – 7z is having two unlike terms (4y and – 7z)
∴ It is a binomial.

(ii) y²
The expression y² is having only one term (y²)
∴ It is a monomial.

(iii) x + y – xy
The expression x + y – xy is having three terms (x, y and – xy)
∴ It is a trinomial.

(iv) 100
The expression 100 is having only one term (100)
∴ It is a monomial.

(v) ab – a – b.
The expression ab – a – b is having three terms (ab, -a, and -b)
∴ The expression is a trinomial.

(vi) 5 – 3t
The expression 5 – 3t is having two terms (5 and -3t)
∴ It is a binomial expression.

(vii) 4p²q – 4pq²
The expression 4p²q – 4pq² is having
two unlike terms (4p²q and – 4pq²)
∴ The expression is a binomial.

(viii) 7mn
The expression 7mn is having only one term (ie 7mn)
∴ The expression is a monomial.

(ix) z²– 3z + 8
The expression z² – 3z + 8 is having three terms (ie z², – 3z and 8)
∴ The expression is a trinomial.

(x) a² + b²
The expression (a² + b²) is having two unlike terms (a² and b²)
∴ It is a binomial expression.

(xi) z² + z
The expression z² + z is having two unlike terms (z2 and z)
∴ The expression in binomial.

(xii) 1 + x + x²
The expression 1 + x + x² is having three terms (1, x and x²)
∴ The expression is a trinomial.

Question 6.
State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) -7x, \(\frac { 5 }{ 2 }\)x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m²p, 4mp²
(vi) 12xz, 12x²z²
Answer:
(i) 1, 100 is a pair of like terms.
(ii) \(\frac { 5 }{ 2 }\)x is a pair of like terms.
(iii) – 29x, – 29y is a pair of unlike terms.
(iv) 14xy, 4²yx is a pair of like terms.
(v) 4m²p, 4mp² is a pair of unlike terms.
(vi) 12xz; 12x²z² is a pair of 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, -7pq, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp,
13p²q, qp²,701p²
Answer:
(a) -xy² and 2xy², – 4yx² and 20x² y, 8x², -11x² and – 6x²; 7y and y; lOOx and 3x; -1 lyx and 2xy are like terms.
(b) 10pq, – 7pq and 78qp.
7p and 2405p; 8q and 100q; – p²q² and 12q²p²; – 23 and 41; – 5p² and 701p²; 13p²q and qp² are like terms.