Question

Write a polynomial that represents the area of the square.

Answer 1

Answer: $x^2+8x+16$

Step-by-step explanation:

It is important to remember that the formula for calculate the area of a square is:

$A=s^2$

Where "s" is the side lenght of the square.

From the figure you can identify that the side lenght of the square can be represented with this expression:

$x+4$

Therefore, the following expression represents the area of the square:

$(x+4)^2$

In order to simplify it, you need to remember that:

$(a\±b)^2=a^2\±2ab+b^2$

Then, you get that the polynomial that represents the area of the given square, is:

$=x^2+2(x)(4)+4^2=x^2+8x+16$