Write the following cubes in expanded form : $(2 x+1)^{3}$
Write the following cubes in expanded form : $(2 x+1)^{3}$
Using Identity $VI$ and Identity $VII,$ we have
$(x+y)^{3}=x^{3}+y^{3}+3 x y(x+y),$ and $(x-y)^{3}=x^{3}-y^{3}-3 x y(x-y)$
$(2 x+1)^{3}=(2 x)^{3}+(1)^{3}+3(2 x)(1)[(2 x)+(1)]$ [Using Identity $VI$]
$=8 x ^{3}+1+6 x [2 x +1] $
$=8 x ^{3}+1+12 x ^{2}+6 x =8 x ^{3}+12 x ^{2}+6 x +1$
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