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Mathematics

Factorise the following:

9x2 - 4(y + 2x)2

Factorisation

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Answer

9x2 - 4(y + 2x)2 = (3x)2 - [2(y + 2x)]2.

Using identity,

a2 - b2 = (a + b)(a - b).

(3x)2 - [2(y + 2x)]2 = [3x + 2(y + 2x)](3x -2(y + 2x))

= (3x + 2y + 4x)(3x - 2y - 4x)

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

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

Hence, 9x2 - 4(y + 2x)2 = -(7x + 2y)(x + 2y).

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