Question

Rewrite in simplest terms: 4, left parenthesis, minus, p, minus, 3, q, right parenthesis, plus, 9, q, minus, 10, left parenthesis, 6, q, plus, 3, p, right parenthesis4(−p−3q)+9q−10(6q+3p)

Answer 1

Let's simplify the expression step by step:

The expression is:

\[ 4(-p - 3q) + 9q - 10(6q + 3p) \]

1. Distribute \(4\) into \(-p - 3q\):
\[
4 \times -p = -4p
\]
\[
4 \times -3q = -12q
\]
So, \(4(-p - 3q) = -4p - 12q\).

2. Now the expression becomes:
\[
-4p - 12q + 9q - 10(6q + 3p)
\]

3. Next, distribute \(-10\) into \(6q + 3p\):
\[
-10 \times 6q = -60q
\]
\[
-10 \times 3p = -30p
\]
So, \(-10(6q + 3p) = -60q - 30p\).

4. Substitute this back into the expression:
\[
-4p - 12q + 9q - 60q - 30p
\]

5. Combine like terms:
Combine \(p\) terms: \(-4p - 30p = -34p\)

Combine \(q\) terms: \(-12q + 9q - 60q = -63q\)

So the simplified expression is:
\[
-34p - 63q
\]