Exercise 12.1 - Chapter 12 Algebraic Expressions class 7 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

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 a and b subtracted from their product.

Answer:

(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) y − y³

(d)   (e) − ab + 2b² − 3a²

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

(a) − 4x + 5 (b) − 4x + 5y (c) 5y + 3y²

(d)   (e) pq + q

(f) 1.2 ab − 2.4 b + 3.6 a (g) 

(h) 0.1p² + 0.2 q²

Answer:

(i)

(a)

(b)

(c)

(d)

(e)

(ii)

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

Answer:

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 (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

Answer:

(a)

(b)

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:

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

Answer:

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, −6x², y, 2xy,3x

(b) 10pq, 7p, 8q, − p²q², − 7qp, − 100q, − 23, 12q²p², − 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Answer:

(a) −xy², 2xy²

−4yx², 20x²y

8x², −11x², −6x²

7y, y

−100x, 3x

−11xy, 2xy

(b) 10pq, −7qp, 78qp

7p, 2405p

8q, −100q

−p²q², 12p²q²

−23, 41

−5p², 701p²

13p²q, qp²