Factorise the following:
a2(b + c) - (b + c)3
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Taking out common in all terms,
(b + c)[a2 - (b + c)2]
Using identity,
a2 - b2 = (a - b)(a + b).
(b + c)[a2 - (b + c)2] = (b + c)(a + b + c)(a - b - c).
Hence, a2(b + c) - (b + c)3 = (b + c)(a + b + c)(a - b - c).
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x3 - 25x
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x2 - 2xy + y2 - a2 - 2ab - b2.