Question

Write a polynomial that represents the area of the figure.

Answer 1

Answer:

$2x^{2} + 8x + 10$

Step-by-step explanation:

Split these into two separate squares.

One has side lengths of x + 3, and the other has side lengths of x + 1.

We'll solve the first square first.

Here is the expression we want to use:

$(x+3)$ * $(x+3)$

Use FOIL (first, outer, inner, last).

$x^{2} + 3x + 3x + 9$

Simplify.

$x^{2} + 6x +9$

Time for the second square!

This goes similarly to the first one, so I'll omit any words and you can follow along with the math.

$(x+1)$ * $(x+1)$

$x^{2} + x + x +1$

$x^{2} + 2x + 1$

Now, we'll add them together.

$x^{2} + 6x +9$ $+$ $x^{2} + 2x + 1$

Combine like terms.

$2x^{2} + 8x + 10$

And we're done!