Question
Factorise:
2a3 + 16b3 - 5a - 10b
2a3 + 16b3 - 5a - 10b
✓
Answer
2a3 + 16b3 - 5a - 10b
= 2(a3 + 8b3) - 5(a + 2b)
= 2[(a)3 + (2b)3] - 5(a + 2b) Since a3 + b3 = (a + b (a2 - a × b + b2)
= 2(a + 2b)[(a)2 - a × 2b + (2b)2] - 5(a + 2b)
= (a + 2b)[2(a2 - 2ab + 4b2) - 5]
= 2(a3 + 8b3) - 5(a + 2b)
= 2[(a)3 + (2b)3] - 5(a + 2b) Since a3 + b3 = (a + b (a2 - a × b + b2)
= 2(a + 2b)[(a)2 - a × 2b + (2b)2] - 5(a + 2b)
= (a + 2b)[2(a2 - 2ab + 4b2) - 5]
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