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

Given:

Dimensions of the rectangle = x² - 4xy + 7y² and x³ - 5xy²

As we know, area of rectangle = l x b

So, putting the value

(x² - 4xy + 7y²) $\times$ (x³ - 5xy²)

= x² $\times$ (x³ - 5xy²) - 4xy $\times$ (x³ - 5xy²) + 7y² $\times$ (x³ - 5xy²)

= x⁽²⁺³⁾ - 5x⁽²⁺¹⁾y² - 4x⁽¹⁺³⁾y + 20x⁽¹⁺¹⁾y⁽¹⁺²⁾ + 7x³y² - 35xy⁽²⁺²⁾

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

= x⁵ + 2x³y² - 4x⁴y + 20x²y³ - 35xy⁴

Hence, the area of the rectangle = x⁵ + 2x³y² - 4x⁴y + 20x²y³ - 35xy⁴