To simplify the expression \((10m - 7)(m + 8)\), we need to use the distributive property, often referred to as the FOIL method, which stands for First, Outer, Inner, and Last.
1. First: Multiply the first terms in each binomial.
[tex]\[
10m \cdot m = 10m^2
\][/tex]
2. Outer: Multiply the outer terms in the binomial.
[tex]\[
10m \cdot 8 = 80m
\][/tex]
3. Inner: Multiply the inner terms in the binomial.
[tex]\[
-7 \cdot m = -7m
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
-7 \cdot 8 = -56
\][/tex]
Now, we combine all these results:
[tex]\[
10m^2 + 80m - 7m - 56
\][/tex]
Next, we combine the like terms \(80m\) and \(-7m\):
[tex]\[
10m^2 + 73m - 56
\][/tex]
Thus, our simplified expression is:
[tex]\[
10m^2 + 73m - 56
\][/tex]
So, the simplified form of [tex]\((10m - 7)(m + 8)\)[/tex] is [tex]\(\boxed{10m^2 + 73m - 56}\)[/tex].
