Question

what is an expression for the perimeter of this rectangle? n^2 + 5n + 6 n^2 - 4

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here $l=n^{2}+5n + 6$ and $w=n^{2}-4$.

Step2: Substitute values into formula

$P=2((n^{2}+5n + 6)+(n^{2}-4))$.

Step3: Simplify inside parentheses

$(n^{2}+5n + 6)+(n^{2}-4)=n^{2}+n^{2}+5n+6 - 4=2n^{2}+5n + 2$.

Step4: Multiply by 2

$P = 2(2n^{2}+5n + 2)=4n^{2}+10n + 4$.

Answer:

$4n^{2}+10n + 4$