CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

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

Question 1.

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

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

Solution:

- y – z
- \(\frac { 1 }{ 2 } \) ( x + y )
- z
^{2} - \(\frac { 1 }{ 4 } \) pq
- x
^{2}+ y^{2} - 3mn + 5
- 10 – yz
- 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

Solution:

(b) 1 + x + x^{2}

Solution:

(c) y – y^{3}

Solution:

(d) 5xy^{2 }+ 7x^{2}y

Solution:

(e) – ab + 2b^{2} – 3a^{2}

Solution:

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

(a) -4x + 5

(b) -4x + 5y

(c) 5y + 3y^{2}

(d) xy + 2x^{2} y^{2}

(e) pq + q

(f) 1.2ab – 2.4b + 3.6a

(g) \(\frac{3}{4}\) x + \(\frac{1}{4}\)

(h) 0.1p^{2} + 0.2q^{2}

Solution:

Question 3.

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

(i) 5 – 3t^{2}

(ii) 1 + t + t^{2} + f^{3}

(iii) x + 2xy + 3y

(iv) 100m + 1000n

(v) – p^{2}q^{2} + 7 pq

(vi) 1.2a + 0.8b

(vii) 3.14r^{2}

(viii) 2 (l + b)

(ix) 0.1y + 0.01y^{2}

Solution:

Question 4.

(a) Identify terms that contain x and give the coefficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x + xy

(vi) 12xy^{2} + 25

(vii) 7x + xy^{2}

Solution:

(b) Identify terms that contain y^{2} and give the coefficient of y^{2}.

(i) 8 – xy^{2}

(ii) 5y^{2 }+ 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

Question 5.

Classify into monomials, binomials, and 4y trinomials

(i) 4y – 7z

(ii) y^{2}

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p^{2}q – 4pq^{2}

(viii) 7mn

(ix) z^{2} – 3z + 8

(x) a^{2} + b^{2}

(xi) z^{2} + z

(xii) 1 + x + x^{2}

Solution:

We know that an algebraic expression containing only one term is called a monomial. So, the monomials are : (ii), (iv), and (viii).

We know that an algebraic expression containing two terms is called a binomial. So, the binomials are : (i), (vi), (vii), (x) and (xi).

We know that an algebraic expression containing three terms is called a trinomial. So, the trinomial are : (iii), (v), (ix) and (xii).

Question 6.

State whether a given pair of terms j is of like or unlike terms:

- 1,100
- -7x, \(\frac { 5 }{ 2 } \) x
- -29 x, -29 y
- 14 xy, 42 yx
- 4m
^{2}p, 4mp^{2} - 12xz, 12x
^{2}z^{2}.

Solution:

- Like
- Like
- Unlike
- Like
- Unlike
- Unlike

Question 7.

Identify like terms in the following:

(a) – xy^{2}, -4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, – 100x, – 11yx, 20x^{2}y, – 6x^{2}, y, 2xy, 3x

Solution:

In the given terms, like terms are grouped as under :

(b) 10pq, 7p, 8q, – p^{2}q^{2}, – 7qp, – 100q,- 23, 12q^{2}p^{2}, – 5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

Solution:

In the given terms, like terms are grouped as under :