PSEB 7th Class Maths Solutions Chapter 12 Algebraic Expressions Ex 12.2

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 12 Algebraic Expressions Ex 12.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.2

1. Fill in the blanks :

(i) 5y + 7y = ……………..
(ii) 3xy + 2xy = ……………..
(iii) 12a² – 7a² = ……………..
(iv) 8mn² – 3mn² = ……………..
Solution:
(i) 12y
(ii) 5xy
(iii) 5a²
(iv) 5mn²

2. Add the following algebraic expressions 

(a) 3xy², 7xy²
Solution:
Given terms are like terms. Their coefficients are 3 and 7.
Required sum is given as :
3xy² + 7xy² = (3 + 7) xy²
= 10xy²

(b) 7x, – 3x, 2x
Solution:
7x + (- 3x) + 2x = (7 – 3 + 2) x
= 6x

(c) 12p²q, 3p²q, – 5p²q
Solution:
(12p²q) + (3p²q) + (- 5p²q)
= (12 + 3 – 5) p²q
= 10p²q

(d) 3x², – 8x², – 5x², 13x²
Solution:
3x² + (- 8x)² + (- 5x)² + 13x²
= (3 – 8 – 5 + 13) x²
= 3x²

3. Add the following algebraic expressions.

(a) x + y and 2x – 3y
Solution:
(a) Horizontal method:
(x + y) + (2x – 3y)
= x + 2x + y – 3y
= 3x – 2y

Column method:

(b) 5a + 7b and 3a – 2b
Solution:
Horizontal method:
(5a + 7b) + (3a – 2b)
= 5a + 3a + 7a – 2b
= 8a + 5b.

Column method:

(c) 3m + 2n, 7m – 8n, 2m – n
Solution:
Horizontal method:
(3m + 2n) + (7m – 8n) + (2m – n)
= 3m + 7m + 2m + 2n – 8n – n
= 12m – 7n

Column method:

(d) 3x² + 2x – 7 and 5x² – 7x + 8
Solution:
Horizontal method:
(3x² + 2x – 7) + (5x² – 7x + 8)
= 3x² + 5x² + 2x – 7x – 1 + 8
= 8x² – 5x + 1

Column method:

(e) m² + 2n² – p², – 3m² + n² + 2p² and 4m² – 3n² + 5p²
Solution:
Horizontal method:
(m² + 2n² – p²) + (- 3m² + n² + 2p²) + (4m² – 3n² + 5p²)
= m² – 3m² + 4m² + 2n² + n² – 3n² – p² + 2p² + 5p²
= 2m² + 0n² + 6p²

Column method:

(f) 3xy + 7x² – 2y², 2xy + y² and 2x² + y²
Solution:
Horizontal method:
(3xy + 7x² – 2y²) + (2xy + y²) + (2x² + y²)
= 3xy + 2xy + 7x² + 2x² – 2y² + y² + y²
= 5xy + 9x² + 0y²

Column method:

4. Simplify the following algebraic expressions by combining like terms.

(a) -5ax + 3xy + 2xy – 8ax
Solution:
– 5ax + 3xy + 2xy – 8ax
= – 5ax – 8ax + 3xy + 2xy
= – 13ax + 5xy.

(b) 3m – 2n + 5m – 3m + 8n
Solution:
3m – 2n + 5m – 3m + 8n
= 3m + 5m – 3m – 2n + 8n
= 5m + 6 n.

(c) 3pq – 15r² – 3l²m² + 2r² + 2l²m² – 5pq
Solution:
3pq – 15r² – 3l²m² + 2r² + 2l²m² – 5pq
= 3pq – 5pq – 15r² + 2r² – 3l²m² + 2l²m²
= – 2pq – 13r² – 2l²m².

(d) 4x³ + 7x² – 3x + 2 – 2x³ – 2x² + 7x – 3
Solution:
4x³ + 7x² – 3x + 2 – 2x³ – 2x² + 7x – 3
= 4x³ – 2x³ + 7x² – 2x² – 3x + 7x + 2 – 3
= 2x³ + 5x² + 4x – 1.

5. Subtract the algebraic expressions.

(a) – 3x² from 7x²
Solution:
7x² – (- 3x²) = 7x² + 3x² = 10x²

(b) – 3ab from 10ab
Solution:
10ab – (- 3ab) = 10ab + 3ab = 13 ab

(c) a + b from a – b
Solution:
(a – b) – (a+ b)
= a – b – a – b
= -2b

(d) 15m + 10n from 2m – 16n
Solution:
2m – 6n – (15m + 10n)
= 2m – 15m – 6n – 10n
= – 13m – 16n

(e) 2x + 8y – 3z from – 3x + 2y + z
Solution:
– 3x + 2y + z – (2x + 8y – 3z)
= – 3x + 2y + z – 2x – 8y + 3z
= – 5x – 6y + 4z

(f) 18m² + 3n² – 2mn – 7 from 3m² – 2n² + 8mn – 8m + 4
Solution:
(3m² – 2n² + 8mn – 8m + 4) – (18m² + 3n² – 2mn – 7)
= 3m² – 2n² + 8mn – 8m + 4 – 18m² – 3n² + 2mn + 7
= 3m² – 18m² – 2n² – 3n² + 8mn + 2mn – 8m + 4 + 7
= – 15m² – 5n² + 10mn – 8m + 11

6. What should be subtracted from l – 2m + 5n to get 2l – 3m + 4n ?
Solution:
(l – 2m + 5n) – (2l – 3m + 4n)
= l – 2l – 2m + 3m + 5n – 4n
= -l + m + n.
Hence, -l + m + n should be subtracted.

7. What should be added to 3x² + 2xy – y² to obtain x² – 7xy + 3y² ?
Solution:
(x² – 7xy + 3y²) – (3x² + 2xy – y²)
= x² – 3x² – 7xy – 2xy + 3y² + y²
= – 2x² – 9xy + 4y².

8. Subtract 3a² + 2b² – 8ab + 8 from the sum of a² – b² + 7ab + 3 and 2a² + 4b² – 18ab + 7
Solution:
First add a² – b² + 7ab + 3 and 2a² + 4b² – 18ab + 7
(a² – b² + 7ab + 3) + (2a² + 4b² – 18ab + 7)
= a² + 2a² – b² + 4b² + 7ab – 18ab + 3 + 7
= 3a² + 3b² – 11ab + 10 …… (1)
Now we subtract 3a² + 2b² – 8ab + 8 from (1)
3a² + 3b² – 11ab + 10 – (3a² + 2b² – 8ab + 8)
= 3a² – 3a² + 3b² – 2b² – 11ab + 8ab + 10 – 8
= 0a² + b² – 3ab + 2
= b² – 3ab + 2

9. How much x² + 3xy + y² is less than 2x² + 5xy – y2 ?
Solution:
(2x² + 5xy – y²) – (x² + 3xy + y²)
= 2x² – x² + 5xy – 3xy – y² – y²
= x² + 2xy – 0y²
Hence, x² + 3xy + y² is less than 2x² + 5xy – y² by x² + 2xy – 2y².

10. Multiple Choice Questions :

Question (i).
The algebraic expression for “Number 5 added to three times the product of numbers m and n” is.
(a) 5 + 3mn
(b) 3 + 5mn
(c) (5 + 3) mn
Answer:
(a) 5 + 3mn

Question (ii).
The sum of algebraic expressions 3x + 11 and 2x – 7 is
(a) 5x + 4
(b) x + 4
(c) 5x – 18
Answer:
(a) 5x + 4

Question (iii).
Subtraction of a + b from 2a + 3b.
(a) a + 2b
(b) – a – 2b
(c) 3a + 4b
(d) a + b
Answer:
(a) a + 2b