NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.5
- Algebraic Expressions and Identities Class 8 Extra Questions
NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3
Ex 9.3 Class 8 Maths Question 1.
Carry out the multiplication of the expressions in each of the following pairs:
(i) 4p, q + r
(ii) ab, a – b
(iii) a + b, 7a
2
b
2
(iv) a
2
– 9, 4a
(v) pq + qr + rp, 0
Solution:
(i) 4p × (q + r) = (4p × q) + (4p × r) = 4pq + 4pr
(ii) ab, a – b = ab × (a – b) = (ab × a) – (ab × b) = a
2
b – ab
2
(iii) (a + b) × 7a
2
b
2
= (a × 7a
2
b
2
) + (b × 7a
2
b
2
) = 7a
3
b
2
+ 7a
2
b
3
(iv) (a
2
– 9) × 4a = (a
2
× 4a) – (9 × 4a) = 4a
3
– 36a
(v) (pq + qr + rp) × 0 = 0
[∵ Any number multiplied by 0 is = 0]
Ex 9.3 Class 8 Maths Question 2.
Complete the table.
|
S.No. |
First Expression |
Second
Expression |
Product |
| (i) | a | b + c + d | – |
| (ii) | x + y – 5 | 5xy | – |
| (iii) | p | 6p 2 – 7p + 5 | – |
| (iv) | 4p 2 q 2 | p 2 – q 2 | – |
| (v) | a + b + c | abc | – |
Solution:
(i) a × (b + c + d) = (a × b) + (a × c) + (a × d) = ab + ac + ad
(ii) (x + y – 5) (5xy) = (x × 5xy) + (y × 5xy) – (5 × 5xy) = 5x
2
y + 5xy
2
– 25xy
(iii) p × (6p
2
– 7p + 5) = (p × 6p
2
) – (p × 7p) + (p × 5) = 6p
3
– 7p
2
+ 5p
(iv) 4p
2
q
2
× (p
2
– q
2
) = 4p
2
q
2
× p
2
– 4p
2
q
2
× q
2
= 4p
4
q
2
– 4p
2
q
4
(v) (a + b + c) × (abc) = (a × abc) + (b × abc) + (c × abc) = a
2
bc + ab
2
c + abc
2
Completed Table:
|
S.No. |
First Expression |
Second
Expression |
Product |
| (i) | a | b + c + d | ab + ac + ad |
| (ii) | x + y – 5 | 5xy | 5x 2 y + 5xy 2 – 25xy |
| (iii) | p | 6p 2 – 7p + 5 | 6p 3 – 7p 2 + 5p |
| (iv) | 4p 2 q 2 | p 2 – q 2 | 4p4q2 – 4p 2 q 4 |
| (v) | a + b + c | abc | a 2 bc + ab 2 c + abc 2 |
Ex 9.3 Class 8 Maths Question 3.
Find the products.
Solution:
Ex 9.3 Class 8 Maths Question 4.
(a) Simplify: 3x(4x – 5) + 3 and find its values for (i) x = 3 (ii) x = \(\frac { 1 }{ 2 }\).
(b) Simplify: a(a
2
+ a + 1) + 5 and find its value for (i) a = 0 (ii) a = 1 (iii) a = -1
Solution:
(a) We have 3x(4x – 5) + 3 = 4x × 3x – 5 × 3x + 3 = 12x
2
– 15x + 3
(i) For x = 3, we have
12 × (3)
2
– 15 × 3 + 3 = 12 × 9 – 45 + 3 = 108 – 42 = 66
(b) We have a(a
2
+ a + 1) + 5
= (a
2
× a) + (a × a) + (1 × a) + 5
= a
3
+ a
2
+ a + 5
(i) For a = 0, we have
= (0)
3
+ (0)
2
+ (0) + 5 = 5
(ii) For a = 1, we have
= (1)
3
+ (1)
2
+ (1) + 5 = 1 + 1 + 1 + 5 = 8
(iii) For a = -1, we have
= (-1)
3
+ (-1)
2
+ (-1) + 5 = -1 + 1 – 1 + 5 = 4
Ex 9.3 Class 8 Maths Question 5.
(a) Add: p(p – q), q(q – r) and r(r – p)
(b) Add: 2x(z – x – y) and 2y(z – y – x)
(c) Subtract: 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)
(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(-a + b + c)
Solution:
(a) p(p – q) + q(q – r) + r(r – p)
= (p × p) – (p × q) + (q × q) – (q × r) + (r × r) – (r × p)
= p
2
– pq + q
2
– qr + r
2
– rp
= p
2
+ q
2
+ r
2
– pq – qr – rp
(b) 2x(z – x – y) + 2y(z – y – x)
= (2x × z) – (2x × x) – (2x × y) + (2y × z) – (2y × y) – (2y × x)
= 2xz – 2x
2
– 2xy + 2yz – 2y
2
– 2xy
= -2x
2
– 2y
2
+ 2xz + 2yz – 4xy
= -2x
2
– 2y
2
– 4xy + 2yz + 2xz
(c) 4l(10n – 3m + 2l) – 3l(l – 4m + 5n)
= (4l × 10n) – (4l × 3m) + (4l × 2l) – (3l × l) – (3l × -4m) – (3l × 5n)
= 40ln – 12lm + 8l
2
– 3l
2
+ 12lm – 15ln
= (40ln – 15ln) + (-12lm + 12lm) + (8l
2
– 3l
2
)
= 25ln + 0 + 5l
2
= 25ln + 5l
2
= 5l
2
+ 25ln
(d) [4c(-a + b + c)] – [3a(a + b + c) – 2b(a – b + c)]
= (-4ac + 4bc + 4c
2
) – (3a
2
+ 3ab + 3ac – 2ab + 2b
2
– 2bc)
= -4ac + 4bc + 4c
2
– 3a
2
– 3ab – 3ac + 2ab – 2b
2
+ 2bc
= -3a
2
– 2b
2
+ 4c
2
– ab + 6bc – 7ac
More CBSE Class 8 Study Material
- NCERT Solutions for Class 8 Maths
- NCERT Solutions for Class 8 Science
- NCERT Solutions for Class 8 Social Science
- NCERT Solutions for Class 8 English
- NCERT Solutions for Class 8 English Honeydew
- NCERT Solutions for Class 8 English It So Happened
- NCERT Solutions for Class 8 Hindi
- NCERT Solutions for Class 8 Sanskrit
- NCERT Solutions