Mathematics
Factorise the following:
x2 - 2xy + y2 - a2 - 2ab - b2.
Factorisation
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Answer
x2 - 2xy + y2 - a2 - 2ab - b2 = (x2 - 2xy + y2) - (a2 + 2ab + b2)
We know that,
(a + b)2 = a2 + 2ab + b2
and
(a - b)2 = a2 - 2ab + b2
∴ (x2 - 2xy + y2) - (a2 + 2ab + b2) = (x - y)2 - (a + b)2.
Using identity,
a2 - b2 = (a - b)(a + b).
(x - y)2 - (a + b)2 = (x - y - a - b)(x - y + a + b).
Hence, x2 - 2xy + y2 - a2 - 2ab - b2 = (x - y - a - b)(x - y + a + b).
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