Question

Factorize x⁴-(x-z)⁴​

Answer 1

Answer:

Step-by-step explanation:

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)

Read more on Brainly.in - https://brainly.in/question/1799726#readmore

Answer 2

x⁴- (x-z)⁴

First lets break this down :

( x² )² - ( x² - z² )²

since its x⁴ - (x² - z²)

we can multiply both the negative signs and well end up with :

( x² )² - ( x² + z² )²

we can continue this sum with the identity ( a² - b² )

and hence end up with :

(x² + x²+ z²) ( x² - x² + z² )

hope this helps