Question
Factorise:
$27 a^3-b^3+8 c^3-18 a b c$
$27 a^3-b^3+8 c^3-18 a b c$
✓
Answer
$27 a^3-b^3+8 c^3-18 a b c$
$=(3 a)^3+(-b)^3+(2 c)^3-3 \times(3 a) \times(-b) \times(2 c)$
$=[3 a+(-b)+2 c]\left[(3 a)^2+(-b)^2+(2 c)^2-3 a(-b) 2 c-3 a \times 2 c\right]$
$=(3 a-b+2 c)\left(9 a^2+b^2+4 c^2+3 a b+2 b c-6 a c\right)$
$=(3 a)^3+(-b)^3+(2 c)^3-3 \times(3 a) \times(-b) \times(2 c)$
$=[3 a+(-b)+2 c]\left[(3 a)^2+(-b)^2+(2 c)^2-3 a(-b) 2 c-3 a \times 2 c\right]$
$=(3 a-b+2 c)\left(9 a^2+b^2+4 c^2+3 a b+2 b c-6 a c\right)$
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