Sure! Let's break down the expression step-by-step to simplify it.
The original expression is:
[tex]\[
-5(3p + 3) + 9(-7 + p)
\][/tex]
Step 1: Distribute the constants inside the parentheses.
Distribute [tex]\(-5\)[/tex] through [tex]\((3p + 3)\)[/tex]:
[tex]\[
-5 \cdot 3p = -15p
\][/tex]
[tex]\[
-5 \cdot 3 = -15
\][/tex]
Similarly, distribute [tex]\(9\)[/tex] through [tex]\((-7 + p)\)[/tex]:
[tex]\[
9 \cdot (-7) = -63
\][/tex]
[tex]\[
9 \cdot p = 9p
\][/tex]
So, after distributing, the expression becomes:
[tex]\[
-15p - 15 - 63 + 9p
\][/tex]
Step 2: Combine like terms.
Combine the [tex]\(p\)[/tex] terms:
[tex]\[
-15p + 9p = -6p
\][/tex]
Combine the constant terms:
[tex]\[
-15 - 63 = -78
\][/tex]
Putting it all together, we get the simplified expression:
[tex]\[
-6p - 78
\][/tex]
So, the equivalent simplified expression is:
[tex]\[
\boxed{-6p - 78}
\][/tex]
Therefore, the correct answer is:
(B) [tex]\(-6p - 78\)[/tex]
