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Question
Factorize 4( x - y)2 -12( x - y)( x + y ) + 9(x + y )2
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Solution
Let ( x - y ) = a, ( x + y ) = b
= 4a2 -12ab + 9b2
Splitting middle term -12 = -6 - 6 also 4 x 9 = -6 x -6
= 4a2 - 6ab - 6ab + 9b2
= 2a (2a - 3b) - 3b (2a - 3b)
= (2a - 3b)(2a - 3b)
= (2a - 3b)2
Substituting a = x - y and b = x + y
=[2 ( x - y ) - 3( x + y )]
= [2x - 2 y - 3x - 3y]2
= [2x - 3x - 2 y - 3y]2
= [-x - 5 y]2
= [(-1)(x + 5y)]2 [∵ (-1)2 = 1]
∴ 4( x - y)2 -12( x - y)( x + y) + 9( x + y )2 = (x + 5y)2
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