Given the following expression:
[tex]X^2-9[/tex]
You can rewrite it in this form:
[tex]=X^2-3^2[/tex]
Because:
[tex]3^2=3\cdot3=9[/tex]
Since both terms are Perfect Squares, you can use the following Difference of two squares Formula in order to factor it:
[tex]a^2-b^2=\mleft(a+b\mright)\mleft(a-b\mright)[/tex]
In this case:
[tex]\begin{gathered} a=X \\ b=3 \end{gathered}[/tex]
Then, substituting and evaluating, you get:
[tex]=(X+3)(X-3)[/tex]
To check it, you can apply the FOIL Method, which states that:
[tex]\mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]
Therefore, you get:
[tex]\begin{gathered} (X+3)(X-3)=(X)(X)+(X)(-3)+(3)(X)+(3)(-3)=X^2-3X+3X-9=X^2-9 \\ \\ \end{gathered}[/tex]
It is correct.
Hence, the answer is:
[tex](X+3)(X-3)[/tex]
