Question

factorize the expressions x⁴-(x-y)⁴​

Answer 1

x⁴-(x-y)⁴

= (x²+(x+y)²}{x²-(x-y)²}

= (x²+x²+2xy+y²)(x+x-y)(x-x+y)

= (2x²+2xy+y²)(2x-y)(y)

= (2x²+2xy+y²)(2xy-y²)

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Answer 2

Answer:

x^4 – (x – y)^4

= (x^2)^2 – [(x – y)^2]^2

= [x^2 – (x – y)^2] [x^2 + (x – y)^2]

= [x + (x – y] [x – (x – y)] [x^2 + x^2 – 2xy + y^2]

= (x + x – y) (x – x + y)[2x^2 – 2xy + y^2]

= (2x – y) y(2x^2 – 2xy + y^2)

= y(2x – y) (2x^2 – 2xy + y^2)