Question

Factorize 4( x - y)²  -12( x - y)( x + y ) + 9(x + y )²

Answer 1

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