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

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Answer 1 · 2018-06-30T17:15:34

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

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

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

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