Question
Factorise:
$2 a^3+16 b^3-5 a-10 b$
$2 a^3+16 b^3-5 a-10 b$
✓
Answer
$2 a^3+16 b^3-5 a-10 b$
$=2\left(a^3+8 b^3\right)-5(a+2 b)$
$=2\left[(a)^3+(2 b)^3\right]-5(a+2 b) \text { Since } a^3+b^3=\left(a+b\left(a^2-a \times b+b^2\right)\right.$
$=2(a+2 b)\left[(a)^2-a \times 2 b+(2 b)^2\right]-5(a+2 b)$
$=(a+2 b)\left[2\left(a^2-2 a b+4 b^2\right)-5\right]$
$=2\left(a^3+8 b^3\right)-5(a+2 b)$
$=2\left[(a)^3+(2 b)^3\right]-5(a+2 b) \text { Since } a^3+b^3=\left(a+b\left(a^2-a \times b+b^2\right)\right.$
$=2(a+2 b)\left[(a)^2-a \times 2 b+(2 b)^2\right]-5(a+2 b)$
$=(a+2 b)\left[2\left(a^2-2 a b+4 b^2\right)-5\right]$
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