Question
Factorise:
8(x + y)3 - 27(x - y)3
8(x + y)3 - 27(x - y)3
✓
Answer
8(x + y)3 - 27(x - y)3
= [23 (x + y)3] - [33 (x - y)3]
= [2(x + y) - 3(x - y)]{[2(x + y)]2 + 2(x + y)3(x - y) + [3(x - y)]2}
= (2x + 2y - 3x + 3y){[4(x2 + y2 + 2xy)] + 6(x2 - y2) + [9(x2 + y2 - 2xy]}
= (-x + 5y){4x2 + 4y2 + 8xy + 6x2 - 6y2 + 9x2 + 9y2 - 18xy}
= (-x + 5y)(19x2 + 7y2 - 10xy)
= [23 (x + y)3] - [33 (x - y)3]
= [2(x + y) - 3(x - y)]{[2(x + y)]2 + 2(x + y)3(x - y) + [3(x - y)]2}
= (2x + 2y - 3x + 3y){[4(x2 + y2 + 2xy)] + 6(x2 - y2) + [9(x2 + y2 - 2xy]}
= (-x + 5y){4x2 + 4y2 + 8xy + 6x2 - 6y2 + 9x2 + 9y2 - 18xy}
= (-x + 5y)(19x2 + 7y2 - 10xy)
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