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] $
$=8 x ^{3}+1+12 x ^{2}+6 x =8 x ^{3}+12 x ^{2}+6 x +1$
Similar Questions
Evaluate the following using suitable identities : $(102)^{3}$
Evaluate the following using suitable identities : $(102)^{3}$
Find the zero of the polynomial : $p(x) = x -5$
Find the zero of the polynomial : $p(x) = x -5$
Use suitable identities to find the products : $(3-2 x)(3+2 x)$
Use suitable identities to find the products : $(3-2 x)(3+2 x)$
Expand each of the following, using suitable identities : $(-2 x+3 y+2 z)^{2}$
Expand each of the following, using suitable identities : $(-2 x+3 y+2 z)^{2}$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+3 x^{3}+3 x^{2}+x+1$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+3 x^{3}+3 x^{2}+x+1$.