Question
Factorise:
$8 a^3+125 b^3-64 c^3+120 a b c$
$8 a^3+125 b^3-64 c^3+120 a b c$
✓
Answer
$8 a^3+125 b^3-64 c^3+120 a b c$
$=(2 a)^3+(5 b)^3+(-4 c)^3-3 \times(2 a) \times(5 b) \times(-4 c)$
$=(2 a+5 b-4 c)\left[(2 a)^2+(5 b)^2+(-4 c)^2-(2 a)(5 b)-(5 b)(-4 c)-(2 a) \times(-4 c)\right]$
$=(2 a+5 b-4 c)\left(4 a^2+25 b^2+16 c^2-10 a b+20 b c+8 a c\right)$
$=(2 a)^3+(5 b)^3+(-4 c)^3-3 \times(2 a) \times(5 b) \times(-4 c)$
$=(2 a+5 b-4 c)\left[(2 a)^2+(5 b)^2+(-4 c)^2-(2 a)(5 b)-(5 b)(-4 c)-(2 a) \times(-4 c)\right]$
$=(2 a+5 b-4 c)\left(4 a^2+25 b^2+16 c^2-10 a b+20 b c+8 a c\right)$
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