Question
Factorise:
(2a + 1)3 + (a - 1)3
(2a + 1)3 + (a - 1)3
✓
Answer
(2a + 1)3 + (a - 1)3
= (2a + 1 + a - 1)[(2a + 1)2 - (2a + 1)(a - 1) + (a - 1)2]
= (3a)[4a2 + 4a + 1 - 2a2 + 2a - a + 1 + a2 - 2a + 1]
= 3a(3a2 + 3a + 3)
= 9a(a2 + a + 1)
= (2a + 1 + a - 1)[(2a + 1)2 - (2a + 1)(a - 1) + (a - 1)2]
= (3a)[4a2 + 4a + 1 - 2a2 + 2a - a + 1 + a2 - 2a + 1]
= 3a(3a2 + 3a + 3)
= 9a(a2 + a + 1)
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