Question
Factorise:
216 + 27b3 + 8c3 - 108bc
216 + 27b3 + 8c3 - 108bc
✓
Answer
216 + 27b3 + 8c3 - 108bc
= (6)3 + (3b)3 + (2c)3 - 3 × 6 × 3b × 2c
= (6 + 3b + 2c)[62 + (3b)2 + (2c)2 - 6 × 3b - 3b × 2c - 2c × 6]
= (6 + 3b + 2c)(36 + 9b2 + 4c2 - 18b - 6bc - 12c)
= (6)3 + (3b)3 + (2c)3 - 3 × 6 × 3b × 2c
= (6 + 3b + 2c)[62 + (3b)2 + (2c)2 - 6 × 3b - 3b × 2c - 2c × 6]
= (6 + 3b + 2c)(36 + 9b2 + 4c2 - 18b - 6bc - 12c)
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