Question

Which polynomial expression represents the area of the outer most square tile, shown below?

Answer 1

ANSWER

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

EXPLANATION

The outermost square tile has side length,

$l = x - 3$

The area of a square is given by;

$Area= {l}^{2}$

We substitite the given expression for the side length into the formula to obtain,

$Area= {(x - 3)}^{2}$

$Area= {(x - 3)}(x - 3)$

We expand using the distributive property to obtain;

$Area=x {(x - 3)} - 3(x - 3)$

This gives us:

$Area= {x}^{2} - 3x - 3x + 9$

$Area= {x}^{2} - 6x + 9$

The last choice is correct.

Answer 2

Hello!

The answer is:

The last option, $x^{2}-6x+9$

Why?

The area of square is given by the following formula:

$Area=l*l=l^{2}$

Where, l is the side of the square, remember that a square has equal sides.

To solve the problem, we must remember the following notable product:

$(a-b)^{2}=a^{2}-2ab+b^{2}$

So, if the side of the given circle is (x-3), the area will be:

$Area=l^{2}=(x-3)^{2}$

Applying the notable product, we have:

$Area=(x-3)^{2}=x^{2} -(2)*(x)(3)+(-3)^{2}\\\\Area=x^{2} -(2)*(x)(3)+(-3)^{2}=x^{2}-6x+9$

So, the correct option is the last option:

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

Have a nice day!