Adjacent Sides Of Rectangle Are X2 4xy 7y2 And X3 5xy2

The adjacent sides of a rectangle are x2 – 4xy + 7y2 and x3 – 5xy2. Find its area.

Answers:

Reqd. area =  (x2 – 4xy + 7y2) (x3 – 5xy2)

= x2(x3 – 5xy2) – 4xy (x3 – 5xy2) + 7y2 (x3 – 5xy2)

= x5 – 5x3y2 – 4x4y + 20x2y3 + 7x3y2 – 35xy4

= x5 + (7 – 5)x3y2 – 4x4y + 20x2y3 – 35xy4

= x5 + 2x3y2 – 4x4y + 20x2y3 – 35xy4

= (x5 – 4x4y + 2x3y2 + 20x2y3 – 35xy4) sq. unit.