Question

factorize x⁴+2x³y-2xy³-y⁴​

Answer 1

Answer:

$\boxed{ \purple{ \bf(x - y)(x + y)(x + y)(x + y)}}$

Step-by-step explanation:

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\tt \:  \longrightarrow \: {x}^{2} - {y}^{2} = (x + y)(x - y)$

$\tt \:  \longrightarrow \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

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$\large\underline\purple{\bold{Solution :- }}$

$\tt \:  \longrightarrow \: {x}^{4} + 2 {x}^{3} y - {2xy}^{3} - {y}^{4}$

$\tt \:  \longrightarrow \: ( {x}^{4} - {y}^{4} ) + (2 {x}^{3} y - {2xy}^{3} )$

$\tt \:  \longrightarrow \: \bigg( {( {x}^{2} )}^{2} - { {(y}^{2}) }^{2} \bigg) + 2xy( {x}^{2} - {y}^{2} )$

$\tt \:  \longrightarrow \: \bigg( ( {x}^{2} - {y}^{2} )( {x}^{2} + {y}^{2}) \bigg) + 2xy( {x}^{2} - {y}^{2} )$

$\tt \:  \longrightarrow \: ( {x}^{2} - {y}^{2} )\bigg( {x}^{2} + {y}^{2} + 2xy \bigg)$

$\tt \:  \longrightarrow \: (x - y)(x + y) {(x + y)}^{2}$

$\tt\implies \: \boxed{ \red{ \bf(x - y)(x + y)(x + y)(x + y)}}$