x^4- (x-z)^4

Question

x⁴-(x-z)⁴

 

 

 

 

 

Answer 1

Hello Mini

 

x⁴-(x-z)⁴

 

x⁴-(x²-2xz+z²)²

 

x⁴ - (x⁴-2x³z+x²z²-2x³z+4x²z²-2xz³+x²z²-2xz³+z⁴)

 

Combine like terms

x4 - (x⁴-4x³z+6x²z²-4xz³+z⁴)

4x³z-6x²z²+4xz³-z⁴

Answer 2

x⁴ - (x - z)⁴ = [x² - (x - z)²][x² + (x - z)²]  (factor as a difference of squares)

 

                  = [x - (x - z)][x + (x - z)][x² + (x² - 2xz + z²)]  (factor again a difference of squares)

 

                  = z(2x - z)(2x² - 2xz + z²)

 

I assumed you needed this factored, yes?