Factorise each of the following : $27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p$
Factorise each of the following : $27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p$
$27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p$ $=(3 p )^{3}-\left(\frac{1}{6}\right)^{3}-3(3 p )\left(\frac{1}{6}\right)\left[3 p -\frac{1}{6}\right]$
$=\left[3 p -\frac{1}{6}\right]^{3}$ [Using Identity $VII$]
$=\left(3 p -\frac{1}{6}\right)\left(3 p -\frac{1}{6}\right)\left(3 p -\frac{1}{6}\right)$
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