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: \[ -34p - 63q \]