Question

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

Answer 1

`3n^4+8n^3+7n^2+2n`

Explanation:

Using the formula

`(a+b)^2=a^2+2ab+b^2`
to get

`(n+1)^2=n^2+2n+1`
and
`n(n^2+2n+1)=n^3+2n^2+n`
now we Need

`(n^3+2n^2+n)(3n+2)=`

`3n^4+6n^3+3n^2+2n^3+4n^2+2n`
collecting like terms to get

`3n^4+8n^3+7n^2+2n`