# NCERT solution class 7 chapter 12 Algebraic expressions 12.1 mathematics

## EXERCISE 12.1

#### Question 1:

Get the algebraicexpressions 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 and b subtracted from their product.

(i) y − z

(ii) (iii) z2

(iv) (v) x2 + y2

(vi) 5 + 3 (mn)

(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) − y3

(d) (e) − ab + 2b2 − 3a2

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

(a) − 4x + 5 (b) − 4x + 5y (c) 5+ 3y2

(d) (e) pq + q

(f) 1.2 ab − 2.4 b + 3.6 (g) (h) 0.1p2 + 0.2 q2

(i)

(a) (b) (c) (d) (e) (ii)

 Row Expression Terms Factors (a) − 4x + 5 − 4x5 − 4, x5 (b) − 4x + 5y − 4x5y − 4, x5, y (c) 5y + 3y2 5y3y2 5, y3, y, y (d) xy + 2x2y2 xy2x2y2 x, y2, x, x, y, y (e) pq + q pqq p, qq (f) 1.2ab − 2.4b + 3.6a 1.2ab− 2.4b3.6a 1.2, a, b− 2.4, b3.6, a (g)          (h) 0.1p2 + 0.2q2 0.1p20.2q2 0.1, p, p0.2, q, q

#### Question 3:

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

(i) 5 − 3t2 (ii) 1 + t2 + t3 (iii) x + 2xy+ 3y

(iv) 100m + 1000n (v) − p2q2 + 7pq (vi) 1.2a + 0.8b

(vii) 3.14 r2 (viii) 2 (b) (ix) 0.1y + 0.01 y2

 Row Expression Terms Coefficients (i) 5 − 3t2 − 3t2 − 3 (ii) 1 + t + t2 + t3 tt2t3 111 (iii) x + 2xy + 3y x2xy3y 123 (iv) 100m + 1000n 100m1000n 1001000 (v) − p2q2 + 7pq − p2q27pq − 17 (vi) 1.2a +0.8b 1.2a0.8b 1.20.8 (vii) 3.14 r2 3.14 r2 3.14 (viii) 2(l + b) 2l2b 22 (ix) 0.1y + 0.01y2 0.1y0.01y2 0.10.01

#### 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 + zx (v) 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

(a)

 Row Expression Terms with x Coefficient of x (i) y2x + y y2x y2 (ii) 13y2 − 8yx − 8yx −8y (iii) x + y + 2 x 1 (iv) 5 + z + zx zx z (v) 1 + x + xy xxy 1y (vi) 12xy2 + 25 12xy2 12y2 (vii) 7x+ xy2 7xxy2 7y2

(b)

 Row Expression Terms with y2 Coefficient of y2 (i) 8 − xy2 −xy2 − x (ii) 5y2 + 7x 5y2 5 (iii) 2x2y + 7y2−15xy2 7y2−15xy2 7−15x

#### 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) 4p2− 4pq2 (viii) 7mn (ix) z2 − 3z + 8

(x) a2 + b2 (xi) z2 + z (xii) 1 + x + x2

The monomials, binomials, and trinomials have 1, 2, and 3 unlike terms in it respectively.

(i) 4y − 7z

Binomial

(ii) y2

Monomial

(iii) x + y − xy

Trinomial

(iv) 100

Monomial

(v) ab − a − b

Trinomial

(vi) 5 − 3t

Binomial

(vii) 4p2q − 4pq2

Binomial

(viii) 7mn

Monomial

(ix) z2 − 3z + 8

Trinomial

(x) a2 + b2

Binomial

(xi) z2 + z

Binomial

(xii) 1 + x + x2

Trinomial

#### Question 6:

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

(i) 1, 100 (ii) (iii) − 29x, − 29y

(iv) 14xy, 42yx (v) 4m2p, 4mp2 (vi) 12xz, 12 x2z2

The terms which have the same algebraic factors are called like terms. However, when the terms have different algebraic factors, these are called unlike terms.

(i) 1, 100

Like

(ii) − 7x Like

(iii) −29x, −29y

Unlike

(iv) 14xy, 42yx

Like

(v) 4m2p, 4mp2

Unlike

(vi) 12xz, 12x2z2

Unlike

#### Question 7:

Identify like terms in the following:

(a) −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2y, 2xy,3x

(b) 10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2qqp2, 701p2

(a) −xy2, 2xy2

−4yx2, 20x2y

8x2, −11x2, −6x2

7yy

−100x, 3x

−11xy, 2xy

(b) 10pq, −7qp, 78qp

7p, 2405p

8q, −100q

p2q2, 12p2q2

−23, 41

−5p2, 701p2

13p2qqp2

error: Content is protected !! 