Answer
8$n^{3}$ + 12$n^{2}$ + 6n + 1
Work Step by Step
$(2n + 1)^{3}$ =
(2n + 1)(2n + 1)(2n + 1) =
Remember that $(a+b)^{2}$ = $a^{2}$ + 2ab + $b^{2}$
So, (2n + 1)(2n + 1)(2n + 1) =
[$(2n)^{2}$ + 2$\times$2n$\times$1 + $1^{2}$](2n + 1) =
(4$n^{2}$ + 4n + 1)(2n + 1) =
Use the distributive property.
4$n^{2}$(2n) +4$n^{2}$(1) +4n(2n) +4n(1) +1(2n) +1(1) =
8$n^{3}$ + 4$n^{2}$ + 8$n^{2}$ + 4n + 2n + 1 =
Simplify.
8$n^{3}$ + 12$n^{2}$ + 6n + 1
