Question

Factorise the following:- please solve (9x^2-4(y+2x)^2)

Answer 1

$\red{ 9x^{2} - 4(y+2x)^{2}} \\= (3x)^{2} - [2(y+2x)]^{2} \\= (3x)^{2} - (2y+4x)^{2} \\= [ 3x + (2y + 4x)] [ 3x - (2y + 4x)]$

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$\blue { (By \: Algebraic\: Identity )}$

$\boxed { \pink { a^{2} - b^{2} = ( a + b )( a - b ) }}$

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$= ( 3x + 2y + 4x) (3x - 2y - 4x)\\= ( 6x + 2y )( -x-2y) \\= -2(3x+y)(x+2y)$

Therefore.,

$\red{ Factors \:of \:9x^{2} - 4(y+2x)^{2}}$

$\green {= -2(3x+y)(x+2y)}$

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