Question

Factorise_
x⁴ - (x - z )⁴​

Answer 1

Answer:

x4-(x-z)4 is the given expression

let (x-z) = y

So, x^4 - y^4 = (x^2)^2 - (y^2)^2 = {(x^2) + (y^2)} {(x^2) - (y^2)} = {(x^2) + (y^2)} (x+y) (x-y)

Put the value of y into the found expression

= {(x^2) + (y^2)} (x+y) (x-y)

= {x^2+(x-z)^2} (x+x-z) (x-x+z)

= (x^2+x^2+z^2-2xz) (2x-z) (z)

= (2x^2+z^2-2xz) (2x-z)(z)

Answer 2

Answer:

z [ 2x² - 2xz + z² ]  [ 2x - z ]

Step-by-step explanation:

x⁴ - (x - z )⁴​

Rewriting it in the format a² - b²:

x⁴ - (x - z )⁴​ = [ x² ]² -  [  (x -z)² ]²

Applying the algebraic identity:  a² - b² = (a + b)(a - b):

x⁴ - (x - z )⁴​ = [ x² + (x - z)² ]  [ x² - (x - z)² ]

Applying (a - b)² = (a² - 2ab + b²):

x⁴ - (x - z )⁴​ = [ x² + (x² - 2xz + z²) ]  [ x² - (x² - 2xz + z²) ]

Simplify:

x⁴ - (x - z )⁴​ = [ x² + x² - 2xz + z² ]  [ x² - x² + 2xz - z² ]

x⁴ - (x - z )⁴​ = [ 2x² - 2xz + z² ]  [ 2xz - z² ]

x⁴ - (x - z )⁴​ = z [ 2x² - 2xz + z² ]  [ 2x - z ]