Question

25(2x-y)^2-16(x-2y)^2

Answer 1

$= > 25 {(2x - y)}^{2} - 16 {(x - 2y)}^{2} \\ \\ = > {[5(2x - y)]}^{2} - [ {4(x - 2y)]}^{2}$
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USING ALGEBRAIC IDENTITY :-

$= > { \alpha }^{2} - { \beta }^{2} = ( \alpha + \beta ).( \alpha - \beta )$
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$= > [ {5(2x - y)]}^{2} - {[4(x - 2y)]}^{2} \\ \\ = >[ (5(2x - y)) + ((4(x - 2y))].[(5(2x - y)) - ((4(x - 2y))] \\ \\ = > (10x - 5y + 4x - 8y).(10x - 5y - 4x + 8y) \\ \\ = > (14x - 13y).(6x + 3y) \\ \\ = > 3(14x - 13y).(2x + y)$
______________________[ANSWER]

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