Question
Factorise:
$7 a^3+56 b^3$
$7 a^3+56 b^3$
✓
Answer
$7 a^3+56 b^3$
$=7\left(a^3+8 b^3\right)$
$=7\left[(a)^3+(2 b)^3\right]$
$=7(a+2 b)\left[a^2-a \times 2 b+(2 b)^2\right] \text { Since } a^3+b^3=(a+b)\left(a^2-a \times b+b^2\right)$
$=7(a+2 b)\left(a^2-2 a b+4 b^2\right)$
$=7\left(a^3+8 b^3\right)$
$=7\left[(a)^3+(2 b)^3\right]$
$=7(a+2 b)\left[a^2-a \times 2 b+(2 b)^2\right] \text { Since } a^3+b^3=(a+b)\left(a^2-a \times b+b^2\right)$
$=7(a+2 b)\left(a^2-2 a b+4 b^2\right)$
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