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Factorisation of Algebraic Expressions — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorisation of Algebraic Expressions2 Marks
Question
Factorize : $16 a^3-\frac{128}{b^3}$
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Answer

$16 a^3-\frac{128}{b^3}$
$=16\left(a^3-\frac{8}{b^3}\right)$
... [Taking out the common factor 16]
$=16\left[a^3-\left(\frac{2}{b}\right)^3\right]$
Here, $\mathrm{A}=\mathrm{a}$ and $\mathrm{B}=\frac{2}{\mathrm{~b}}$
$\begin{aligned}
& \therefore \quad 16 \mathrm{a}^3-\frac{128}{b^3}=16\left(\mathrm{a}-\frac{2}{b}\right)\left[\mathrm{a}^2+a\left(\frac{2}{b}\right)+\left(\frac{2}{b}\right)^2\right] \\
& \cdots\left[\because A^3-B^3=(A-B)\left(A^2+A B+B^2\right)\right] \\
&=16\left(a-\frac{2}{b}\right)\left(a^2+\frac{2 a}{b}+\frac{4}{b^2}\right)
\end{aligned}$

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