Question

the dimensions of a rectangle are shown. write the area of the rectangle as a sum of cubes. the area of the rectangle as a sum of cubes is

Explanation:

Step1: Recall area formula for rectangle

The area $A$ of a rectangle is given by $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=x^{2}-3x + 9$ and $w=x + 3$.

Step2: Use the distributive property (FOIL - like for polynomials)

$(x + 3)(x^{2}-3x + 9)=x(x^{2}-3x + 9)+3(x^{2}-3x + 9)$.
First, $x(x^{2}-3x + 9)=x^{3}-3x^{2}+9x$. Second, $3(x^{2}-3x + 9)=3x^{2}-9x + 27$.

Step3: Combine like - terms

$(x^{3}-3x^{2}+9x)+(3x^{2}-9x + 27)=x^{3}+(-3x^{2}+3x^{2})+(9x-9x)+27$.
The $-3x^{2}$ and $3x^{2}$ cancel out, and the $9x$ and $-9x$ cancel out.

Answer:

$x^{3}+27$