To solve the given expression [tex]\((m-7)(m+2)\)[/tex], we will use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last). Here is the detailed step-by-step solution:
1. First Terms (F):
Multiply the first terms in each binomial:
[tex]\[
m \cdot m = m^2
\][/tex]
2. Outer Terms (O):
Multiply the outer terms in the binomials:
[tex]\[
m \cdot 2 = 2m
\][/tex]
3. Inner Terms (I):
Multiply the inner terms in the binomials:
[tex]\[
-7 \cdot m = -7m
\][/tex]
4. Last Terms (L):
Multiply the last terms in each binomial:
[tex]\[
-7 \cdot 2 = -14
\][/tex]
5. Combine All Terms:
Now, we need to sum all these products together:
[tex]\[
m^2 + 2m - 7m - 14
\][/tex]
6. Simplify the Expression:
Combine the like terms ([tex]\(2m\)[/tex] and [tex]\(-7m\)[/tex]):
[tex]\[
m^2 + (2m - 7m) - 14 = m^2 - 5m - 14
\][/tex]
So, the simplified form of the expression [tex]\((m-7)(m+2)\)[/tex] is:
[tex]\[
m^2 - 5m - 14
\][/tex]
