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

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.

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

Solution:

1. y – z
2. \(\frac { 1 }{ 2 } \) ( x + y )
3. z²
4. \(\frac { 1 }{ 4 } \) pq
5. x² + y²
6. 3mn + 5
7. 10 – yz
8. 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 + x²
Solution:

(c) y – y³
Solution:

(d) 5xy² + 7x²y
Solution:

(e) – ab + 2b² – 3a²
Solution:

(ii) Identify terms and factors in the expressions given below :
(a) -4x + 5
(b) -4x + 5y
(c) 5y + 3y²
(d) xy + 2x² y²
(e) pq + q
(f) 1.2ab – 2.4b + 3.6a
(g) \(\frac{3}{4}\) x + \(\frac{1}{4}\)
(h) 0.1p² + 0.2q²
Solution:

Question 3.
Identify the numerical coefficients terms (other than constants) in the following expressions :
(i) 5 – 3t²
(ii) 1 + t + t² + f³
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p²q² + 7 pq
(vi) 1.2a + 0.8b
(vii) 3.14r²
(viii) 2 (l + b)
(ix) 0.1y + 0.01y²
Solution:

Question 4.
(a) Identify terms that 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
Solution:

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

Question 5.
Classify into monomials, binomials, and 4y 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
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. 1,100
2. -7x, \(\frac { 5 }{ 2 } \) x
3. -29 x, -29 y
4. 14 xy, 42 yx
5. 4m²p, 4mp²
6. 12xz, 12x² z².

Solution:

1. Like
2. Like
3. Unlike
4. Like
5. Unlike
6. Unlike

Question 7.
Identify like terms in the following:
(a) – xy², -4yx², 8x², 2xy², 7y, – 11x², – 100x, – 11yx, 20x²y, – 6x², y, 2xy, 3x
Solution:
In the given terms, like terms are grouped as under :

(b) 10pq, 7p, 8q, – p²q², – 7qp, – 100q,- 23, 12q²p², – 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Solution:
In the given terms, like terms are grouped as under :