Question
Factorise:
$3 a^7 b-81 a^4 b^4$
$3 a^7 b-81 a^4 b^4$
✓
Answer
$3 a^7 b-81 a^4 b^4$
$=3 a^4 b\left(a^3-27 b^3\right)$
$=3 a^4 b\left[(a)^3-(3 b)^3\right]$
$=3 a^4 b(a-3 b)\left[(a)^2+a \times 3 b+(3 b)^2\right] \text { Since } a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
$=3 a^4 b(a-3 b)\left(a^2+3 a b+9 b^2\right)$
$=3 a^4 b\left(a^3-27 b^3\right)$
$=3 a^4 b\left[(a)^3-(3 b)^3\right]$
$=3 a^4 b(a-3 b)\left[(a)^2+a \times 3 b+(3 b)^2\right] \text { Since } a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
$=3 a^4 b(a-3 b)\left(a^2+3 a b+9 b^2\right)$
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