# NCERT Solution For Class 8 Maths Chapter – Algebraic Expression Exercise – 9.4

### Q1. Multiply the binomials.

• (2x + 5) and (4x – 3)
• (y – 8) and (3y – 4)
• (2.5l – 0.5m) and (2.5l + 0.5m)
• (a + 3b) and (x + 5)
• (2pq + 3q2) and (3pq – 2q2)
• (3/4 a2 + 3b2) and 4(a2 – 2/3b2)

### Solution:-

• (2x + 5) (4x – 3)

= 2x x 4x – 2x x 3 + 5 x 4x – 5 x 3

= 8x2 + 14x – 15

• ( y – 8) (3y – 4)

= y x 3y – 4y – 8 x 3y + 32

= 3y2  – 28y + 32

• (2.5l
– 0.5m) (2.5l + 0.5m)

=  2.5 L X 2.5L + 2.5L X 0.5M – 0.5M X 2.5L – 0.5M X 0.5M

= 6.25L2 – 0.25 M2

(IV) (a + 3b) ( x+ 5)

= ax + 5a + 3bx + 15b

• (a + 3b) (x + 5)

= ax + 5a + 3bx + 15b

• (2pq + 3q2) (3pq – 2q2)

= 6p2q2 + 5pq3 – 6q4

• (3/4 a2 + 3b2) and 4(a2 – 2/3b2)

= 3a4 + 10a2b2  – 8b4

### Q2.  Find the product.

• ( 5 – 2x) (3 + x)
• (x + 7y) (7x – y)
• (a2 + b) ( a + b2)
• (p2 – q2) (2p + q)

### Solution:-

• = 5(3 + x ) -2x (3 + x)

= 15 – x – 2x2

• = x(7x – y) + 7y (7x – y)

= 7x2 – 7y+ 48xy

• = a2 (a + b2) + b (a + b2)

= a3 + b3 + a2b2 + ab

• = p2 (2p + q) -q2 (2p + q)

= 2p3 – q3 + p2q -2pq2

### Q3. Simplify.

• (x2 – 5) (x + 5) + 25
• (a2 + 5) (b3 + 3) + 5
• (t + s2) (t2 – s)
• (a + b) (c – d) + (a – b ) ( c + d) + 2(ac + bd)
• ( x + y )(2x + y ) + (x + 2y)(x – y )
• (x + y ) (x2 – xy + y2)
• (1.5x – 4y) (1.5x + 4y + 3) -4.5x + 12y
• ( a+ b + c) (a + b – c )

### Solution:-

• = x3 + 5x2 – 5x – 25 + 25

= x3 + 5x2 – 5x

• = a2b3 + 3a2 + 5b3 +15 + 5

= a2b3 + 5b3 + 3a2 + 20

• = t (t2 – s) + s2 (t2 – s)

= t3 – s3 – st + s2t2

• = (a + b )(c – d) + (a – b) (c + d) + 2( ac + bd)

= 4ac

• = 2x2 +xy + 2xy + y2 + x2 – xy + 2xy – 2y2

= 3x2 + 4xy – y2

• = x – x2y + xy2 + x2y – xy2 + y3

= x3 + y3

• = 2.25x2 + 6xy + 4.5x – 6xy – 16y2 – 12y

= 2.25x2 – 16y2

• (a + b + c)(a + b – c)

= a2 + ab – ac + ab + b2 – bc + ac + bc – c2

= a2 + b2 – c2 + 2ab