Factorise : \(16(2x - y)^2 - 24(4x^2 - y^2) + 9(2x + y)^2\)

1.	Factorise : \(16(2x - y)^2 - 24(4x^2 - y^2) + 9(2x + y)^2\)
Answer» \(16(2x - y)^2 - 24(4x^2 - y^2) + 9(2x + y)^2\) = \((4(2x-y)^2-2\times4\times3x(2x-y)\times(2x+y)+(3(2x+y))^2\) = \([4(2x-y)-3(2x+y)]^2\) [∴ a² - 2ab + b² = (a - b)²] = [ 8x - 4y - 6x - 3y]² = (2x - 7y)(2x - 7y).

Answer»

\(16(2x - y)^2 - 24(4x^2 - y^2) + 9(2x + y)^2\)

= \((4(2x-y)^2-2\times4\times3x(2x-y)\times(2x+y)+(3(2x+y))^2\)

= \([4(2x-y)-3(2x+y)]^2\) [∴ a² - 2ab + b² = (a - b)²]

= [ 8x - 4y - 6x - 3y]²

= (2x - 7y)(2x - 7y).

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