Question

Please use the foil method to answer this
`{x}^(2) - 9`

Answer 1

Given the following expression:

`X^2-9`

You can rewrite it in this form:

`=X^2-3^2`

Because:

`3^2=3\cdot3=9`

Since both terms are Perfect Squares, you can use the following Difference of two squares Formula in order to factor it:

`a^2-b^2=\mleft(a+b\mright)\mleft(a-b\mright)`

In this case:

`\begin{gathered} a=X \\ b=3 \end{gathered}`

Then, substituting and evaluating, you get:

`=(X+3)(X-3)`

To check it, you can apply the FOIL Method, which states that:

`\mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd`

Therefore, you get:

`\begin{gathered} (X+3)(X-3)=(X)(X)+(X)(-3)+(3)(X)+(3)(-3)=X^2-3X+3X-9=X^2-9 \\ \\ \end{gathered}`

It is correct.

Hence, the answer is:

`(X+3)(X-3)`