Mathematics
Factorise the following:
9x4 - (x2 + 2x + 1)
Factorisation
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Answer
9x4 - (x2 + 2x + 1) = (3x2)2 - (x + 1)2.
Using identity,
a2 - b2 = (a - b)(a + b).
(3x2)2 - (x + 1)2 = (3x2 - x - 1)(3x2 + x + 1).
Hence, 9x4 - (x2 + 2x + 1) = (3x2 - x - 1)(3x2 + x + 1).
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