Question
Factorise:
$125 a^3+b^3+64 c^3-60 a b c$
$125 a^3+b^3+64 c^3-60 a b c$
✓
Answer
$125 a^3+b^3+64 c^3-60 a b c$
$=(5 a)^3+(b)^3+(4 c)^3-3 \times 5 a \times b \times 4 c$
$=(5 a+b+4 c)\left[(5 a)^2+(b)^2+(4 c)^2-5 a \times b-b \times 4 c-5 a \times 4 c\right]$
$=(5 a+b+4 c)\left(25 a^2+b^2+16 c^2-5 a b-4 b c-20 a c\right.$
$=(5 a)^3+(b)^3+(4 c)^3-3 \times 5 a \times b \times 4 c$
$=(5 a+b+4 c)\left[(5 a)^2+(b)^2+(4 c)^2-5 a \times b-b \times 4 c-5 a \times 4 c\right]$
$=(5 a+b+4 c)\left(25 a^2+b^2+16 c^2-5 a b-4 b c-20 a c\right.$
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