To simplify the expression [tex]\( 5(-4p - 8p + 3) - 7p \)[/tex], follow these steps:
1. Distribute the 5 within the parentheses:
[tex]\[
5(-4p - 8p + 3) = 5 \cdot (-4p) + 5 \cdot (-8p) + 5 \cdot 3
\][/tex]
This results in:
[tex]\[
5 \cdot (-4p) = -20p \\
5 \cdot (-8p) = -40p \\
5 \cdot 3 = 15
\][/tex]
2. Combine these distributed terms together:
[tex]\[
-20p - 40p + 15
\][/tex]
3. Combine like terms within the result:
[tex]\[
-20p - 40p = -60p \\
\][/tex]
Thus, we have:
[tex]\[
-60p + 15
\][/tex]
4. Subtract the remaining term from the expression:
Note that we still need to account for the [tex]\(-7p\)[/tex] that was initially outside the parentheses. Incorporate this term into the expression:
[tex]\[
-60p + 15 - 7p
\][/tex]
Combine the [tex]\( p \)[/tex]-terms:
[tex]\[
-60p - 7p = -67p
\][/tex]
Therefore, the final simplified expression is:
[tex]\[
-67p + 15
\][/tex]
So, the simplified form of the expression [tex]\( 5(-4p - 8p + 3) - 7p \)[/tex] is:
[tex]\[
-67p + 15
\][/tex]
