Sure, let's break this down using the FOIL method, which stands for First, Outer, Inner, and Last terms in the binomial multiplication:
1. First Terms:
Multiply the first terms of each binomial:
[tex]\[
x \cdot x = x^2
\][/tex]
2. Outer Terms:
Multiply the outer terms of each binomial:
[tex]\[
x \cdot (-5) = -5x
\][/tex]
3. Inner Terms:
Multiply the inner terms of each binomial:
[tex]\[
-7 \cdot x = -7x
\][/tex]
4. Last Terms:
Multiply the last terms of each binomial:
[tex]\[
-7 \cdot (-5) = 35
\][/tex]
Now, combine these results:
[tex]\[
x^2 - 5x - 7x + 35
\][/tex]
Combine like terms:
[tex]\[
x^2 - 12x + 35
\][/tex]
So, the final simplified expression is:
[tex]\[
x^2 - 12x + 35
\][/tex]
Let's fill in the table accordingly:
\begin{tabular}{|c|c|c|c|c|}
\hline
Expression & First & Outer & Inner & Last \\
\hline
[tex]$(x-7)(x-5)$[/tex] & [tex]$x^2$[/tex] & [tex]$-5x$[/tex] & [tex]$-7x$[/tex] & 35 \\
\hline
\end{tabular}
The resulting simplified expression is:
[tex]\[
x^2 - 12x + 35
\][/tex]
