Question

Simplify the expression:
9(–c^2+5c)+–4(7+–6c^2)

Answer 1

To simplify the expression \( 9(–c^2+5c) + –4(7+–6c^2) \), we will follow these steps:

1. Distribute the constants to the terms inside the parentheses.
2. Combine like terms.

Let's do it step by step.

**Step 1:** Distribute \( 9 \) to \( -c^2 + 5c \) and \( -4 \) to \( 7 + -6c^2 \).

\[
9(-c^2) + 9(5c) + -4(7) + -4(-6c^2)
\]

Calculating each term:

\[
9(-c^2) = -9c^2
\]

\[
9(5c) = 45c
\]

\[
-4(7) = -28
\]

\[
-4(-6c^2) = 24c^2
\]

So, substituting these values back, our expression becomes:

\[
-9c^2 + 45c - 28 + 24c^2
\]

**Step 2:** Combine like terms. We have the \( c^2 \) terms and the constant term:

Combine the \( c^2 \) terms:

\[
-9c^2 + 24c^2 = 15c^2
\]

Now add this to the \( 45c \) term and the constant:

\[
15c^2 + 45c - 28
\]

So the simplified expression is:

\[
\boxed{15c^2 + 45c - 28}
\]