Question

Factorise x^4-(x-z)^4​

Answer 1

Answer:

(2x²-2xz+z²)(2xz-z²)

Step-by-step explanation:

x⁴ - (x-z)⁴

= (x²)² - {(x-z)²}²

According to identity a² - b² = (a+b)(a-b)

(x²)² - {(x-z)²}²

= {x² + (x-z)²}{x² - (x-z)²}

{x² + (x²-2xz + z²)}{x²- (x²-2xz+z²)} {x² + x²-2xz +z²}{x² - x²+2xz - z²}

= {2x² -2xz + z²)(2xz - z²)

Hope it helps you.