Question 1.

Multiply:

i. 16xy × 18xy

ii. 23xy² × 4yz²

iii. (12a + 17b) × 4c

iv. (4x + 5y) × (9x + 7y)

Solution:

i. 16xy × 18xy

= 16 × 18 × xy × xy

= 288x²y²

ii. 23xy² × 4yz²

= 23 × 4 × xy² × yz²

= 92xy³z²

iii. (12a + 17b) × 4c = 12a × 4c + 17b × 4c

= 48ac + 68bc

iv. (4x + 5y) × (9x + 7y)

= 4x × (9x + 7y) + 5y × (9x + 7y)

= (4x × 9x) + (4x × 7y) + (5y × 9x) + (5y × 7y)

= 36x² + 28xy + 45xy + 35y²

= 36x² + 73xy + 35y²

Question 2.

A rectangle is (8x + 5) cm long and (5x + 3) cm broad. Find its area. Solution:

Length of the rectangle = (8x + 5) cm

Breadth of the rectangle = (5x + 3) cm

∴ Area of the rectangle = length × breadth

= (8x + 5) × (5x + 3)

= 8x × (5x + 3) + 5 × (5x + 3)

= (8x × 5x) + (8x × 3) + (5 × 5x) + (5 × 3)

= 40x² + 24x + 25x + 15

= 40x² + 49x + 15

∴ The area of the rectangle is (40x² + 49x + 15) sq. cm.