Using the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , find the value of $(2 x + 4 y) (2 x - 4 y)$

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Solution

WE need to factorise $(2 x + 4 y) (2 x - 4 y)$
Given identity is $(x + a) (x + b) = x^{2} + (a + b) x + a b$
Here $x = 2 x, a = b = 4 y$
Thus we have $(2 x + 4 y) (2 x - 4 y) = (2 x)^{2} + (4 y - 4 y) + (4 y) (- 4 y) = 4 x^{2} - 16 y^{2}$

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