Ncert Solutions for Algebraic Expressions and Identities Class 8 Maths Chapter 9 Exercise 9.4

Question 1
 Multiply the binomials.
i) (2x + 5) and (4x – 3)
 (ii) (y – 8) and (3y – 4)
 (iii) (2.5l – 0.5m) and (2.5l + 0.5m)
 (iv) (a + 3b) and (x + 5)
 (v) (2pq + 3q²) and (3pq – 2q²)
Answer: Let  ( a+b) (c+d) to be done
then
( a+b) (c+d)= a(c+d) + b( c+d)
=a x  c+a x  d+b x  c+b x d
We will use the same concept in all the question below
i) (2x + 5)(4x - 3)
= 2x x 4x - 2x x 3 + 5 x 4x - 5 x 3
= 8x² - 6x + 20x -15
= 8x² + 14x -15
ii) ( y - 8)(3y - 4)
= y x 3y - 4y - 8 x 3y + 32
= 3y² - 4y - 24y + 32
= 3y² - 28y + 32
iii) (2.5l - 0.5m)(2.5l + 0.5)
Using (a+b)(a-b) = a² - b²
We get = 6.25l² - 0.25m²
iv) ax + 5a + 3bx + 15b
v) 2pq x 3pq - 2pq x 2q² + 3q² x 3pq - 3q² x 2q²
= 6p²q² - 4pq³ + 9pq³ - 6q⁴ = 6p²q² - 5pq³ - 6p⁴
Question 2
Find the product.
(i) (5 – 2x) (3 + x)
 (ii) (x + 7y) (7x – y)
iii) (a²+ b) (a + b²)
 (iv) (p²– q²) (2p + q)
Answer: i) 15 + 5x - 6x - 2x²
= 15 - x - x ²
ii) 7x² - xy + 49xy - 7y²
= 7x² - 7y² + 48xy
iii) a² x a + a² x b + a x b + b³
= a³ + a²b + ab + b³
= a³ + b³ + a²b + ab
iv) 2p³ + p²q - 2pq² - q³
= 2p³ - q³ + p²q - 2pq²

Question 3
 Simplify.
(i) (x²– 5) (x + 5) + 25
 (ii) (a²+ 5) (b³+ 3) + 5
 (iii) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
 (iv) (x + y)(2x + y) + (x + 2y)(x – y)
 (v) (x + y)(x²– xy + y²)
 (vi) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
 (vii) (a + b + c)(a + b – c)
Answer:
i) x³ + 5x² - 5x - 25 + 25
= x3 + 5x² -5x
ii) a²b³ + 3a² + 5b³ + 15 + 5
= a²b³ + 5b³ + 3a² + 20
iii) (ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)
= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
= 4ac
iv) 2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²
= 3x² + 4xy - y²
v) x³ - x²y + xy² + x²y - xy² + y³
= x³ + y³
vi) 2.25x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y
= 2.25x² - 16y²
vii) a² + ab - ac + ab + b² - bc + ac + bc - c²
= a² + b² - c² + 2ab

Download Algebraic Expressions Exercise 9.4 as pdf


Class 8 Maths Class 8 Science