Write the following cubes in expanded form : $(2 a-3 b)^{3}$
Write the following cubes in expanded form : $(2 a-3 b)^{3}$
Using Identity $VI$ and Identity $VII,$ we have
$(x+y)^{3}=x^{3}+y^{3}+3 x y(x+y),$ and $(x-y)^{3}=x^{3}-y^{3}-3 x y(x-y)$
$(2 a-3 b)^{3}=(2 a)^{3}-(3 b)^{3}-3(2 a)(3 b)[(2 a)-(3 b)]$
$=8 a ^{3}-27 b ^{3}-18 ab (2 a -3 b )$ [Using Identity $VII$]
$=8 a^{3}-27 b^{3}-\left[36 a^{2} b-54 a b^{2}\right]=8 a^{3}-27 b^{3}-36 a^{2} b+54 a b^{2}$
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