# How do you simplify n( n + 1) ^ { 2} ( 3n + 2)?

Jun 30, 2018

$3 {n}^{4} + 8 {n}^{3} + 7 {n}^{2} + 2 n$

#### Explanation:

Using the formula

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$
to get

${\left(n + 1\right)}^{2} = {n}^{2} + 2 n + 1$
and
$n \left({n}^{2} + 2 n + 1\right) = {n}^{3} + 2 {n}^{2} + n$
now we Need

$\left({n}^{3} + 2 {n}^{2} + n\right) \left(3 n + 2\right) =$

$3 {n}^{4} + 6 {n}^{3} + 3 {n}^{2} + 2 {n}^{3} + 4 {n}^{2} + 2 n$
collecting like terms to get

$3 {n}^{4} + 8 {n}^{3} + 7 {n}^{2} + 2 n$