Question

The area of a rectangle is expressed as ​x4​ ​ − 16​y^4​, determine & state the length and the width of the rectangle, expressed as polynomials.

Answer 1

Explanation:

16 = 2 *2 * 2 * 2 = 2⁴

16y⁴ = (2y)⁴

x⁴ - 16y⁴ = x⁴ - (2y)⁴

= (x²)² - [ (2y)² ]²

{Use identity = a² -b² =(a +b)(a- b). Here a =x² & b =(2y)²}

= (x² + (2y)² ) (x² - (2y)² )

= (x² + 4y²) (x² - 4y²)