Question
Factorise:
$(a+b)^3-(a-b)^3$
$(a+b)^3-(a-b)^3$
✓
Answer
We know that, Since $a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
Therefore,
$(a+b)^3-(a-b)^3$
$=[a+b-(a-b)]\left[(a+b)^2+(a+b)(a-b)+(a-b)^2\right.$
$=(a+b-a+b)\left[a^2+b^2+2 a b+a^2-b^2+a^2+b^2-2 a b\right]$
$=2 b\left(3 a^2+b^2\right)$
Therefore,
$(a+b)^3-(a-b)^3$
$=[a+b-(a-b)]\left[(a+b)^2+(a+b)(a-b)+(a-b)^2\right.$
$=(a+b-a+b)\left[a^2+b^2+2 a b+a^2-b^2+a^2+b^2-2 a b\right]$
$=2 b\left(3 a^2+b^2\right)$
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