Question

Factor the expression x4 − y4 using the polynomial identity (x2 − y2) = (x − y)(x + y). Hint: x4 = (x2)2 and y4 = (y2)2.

Answer 1

Answer:

(x - y)(x + y)(x² + y²)

Step-by-step explanation:

$x^{4}$ - $y^{4}$ ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

$x^{4}$ - $y^{4}$

= (x²)² - (y²)²

= (x² - y²)(x² + y²) ← x² - y² is also a difference of squares, then

= (x - y)(x + y)(x² + y²)