Question

Factor Completely x^4-2x^2y^2+y^4

100 Points pls help me and i will give the brainliest also pls if u can attach maybe some easier ways to solve problems like these...

Answer 1

Answer :

$\bf (x+y)^2(x-y)^2$

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Solving Steps:

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$\rightarrow \sf x^4-2x^2y^2+y^4$

breakdown

$\rightarrow \sf x^4-x^2y^2-x^2y^2+y^4$

factor common term

$\rightarrow \sf x^2(x^2-y^2)-y^2(x^2-y^2)$

collect in groups

$\rightarrow \sf (x^2-y^2)(x^2-y^2)$

apply difference between two square method: x² - y² = (x+ y)(x-y)

$\rightarrow \sf (x+y)(x-y) (x+y)(x-y)$

simplify

$\rightarrow \sf (x+y)^2(x-y)^2$