Question

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

Answer 1

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

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

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

= x⁵ + 2x³y² –  4x⁴y + 20x²y³ – 35xy⁴

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