Question

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

Answer 1

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!

Answer 2

`{x}^(2) - 6x + 9`

Step-by-step 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.