Mathematics
Factorise the following:
9x4 - x2 - 12x - 36
Factorisation
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Answer
9x4 - x2 - 12x - 36 = 9x4 - (x2 + 12x + 36).
The above equation can be written as,
9x4 - [x2 + (2 × 6 × x) + (6)2]
As, (a + b)2 = a2 + 2ab + b2.
∴ 9x4 - [x2 + (2 × 6 × x) + (6)2] = (3x2)2 - (x + 6)2.
Using identity,
a2 - b2 = (a - b)(a + b)
(3x2)2 - (x + 6)2 = (3x2 + x + 6)(3x2 - x - 6).
Hence, 9x4 - x2 - 12x - 36 = (3x2 + x + 6)(3x2 - x - 6).
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