Question

a rectangle has a height of x + 9 and a width of x^2 + 2x. express the area of the entire rectangle. your answer should be a polynomial in standard form. area =

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is given by $A = \text{height}\times\text{width}$. Here, height $h=x + 9$ and width $w=x^{2}+2x$. So $A=(x + 9)(x^{2}+2x)$.

Step2: Use distributive property

$(x + 9)(x^{2}+2x)=x(x^{2}+2x)+9(x^{2}+2x)$.

Step3: Distribute again

$x(x^{2}+2x)=x^{3}+2x^{2}$ and $9(x^{2}+2x)=9x^{2}+18x$.

Step4: Combine like - terms

$A=x^{3}+2x^{2}+9x^{2}+18x=x^{3}+(2x^{2}+9x^{2})+18x=x^{3}+11x^{2}+18x$.

Answer:

$x^{3}+11x^{2}+18x$