Question

Factorize ;
$(x - 2y) {}^{2} + 4x - 8y$
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Answer 1

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$

Factorize ;

$(x - 2y) {}^{2} + 4x - 8y$

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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$= > {(x - 2y)}^{2} + 4x - 8y$

=>here ,this identity is used

$\bold{\red{= > {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}$

$= > {(x - 2y)}^{2} = {x}^{2} + {(2y)}^{2} - 2(x)(2y) = {x}^{2} + 4 {y}^{2} - 4xy$

Now,come to the Question:-

$= > {(x - 2y)}^{2} + 4x - 8y$

$= > {x}^{2} + 4 {y}^{2} - 4xy + 4x - 8y$

$= > {x}^{2} + 4x - 4xy + 4 {y}^{2} - 8y$

$\bold{\boxed{= > {x}^{2} + 4x(1 - y) + 4y(y - 2)}}$

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