Mathematics
Factorise the following:
9x2 + 12x + 4 - 16y2
Factorisation
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Answer
9x2 + 12x + 4 - 16y2 = (3x)2 + (2 × 3x × 2) + 22 - (4y)2
We know that,
(a + b)2 = a2 + b2 + 2ab.
∴ (3x)2 + (2 × 3x × 2) + 22 - (4y)2 = (3x + 2)2 - (4y)2
We know that,
a2 - b2 = (a + b)(a - b).
∴ (3x + 2)2 - (4y)2 = (3x + 2 + 4y)(3x + 2 - 4y).
Hence, 9x2 + 12x + 4 - 16y2 = (3x + 2 + 4y)(3x + 2 - 4y).
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