We have, #10; #10; #10;a^2 ( 2a+3b )^2 =( a ( #10;2a+3b ) )( a+( 2a+3b ) #10;) ∴ #10;a^2 b^2=( a+b )( a b ) #10; #10; ...

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Question

Solve:
$a^{2} - (2 a + 3 b)^{2}$

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Solution

We have,

$a^{2} - {(2 a + 3 b)}^{2}$ $= (a - (2 a + 3 b)) (a + (2 a + 3 b)) ∴ a^{2} - b^{2} = (a + b) (a - b)$

$= (a - 2 a - 3 b) (a + 2 a + 3 b)$

$= (- a - 3 b) (3 a + 3 b)$

$= - 3 (a + 3 b) (a + b)$
Hence, this is the answer.

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