Questions: Simplify 1/3 q(-12 q-9). -4 q+27 q -36 q+3 q -36 q^2-27 q -4 q^2-3 q

Solution Steps

To simplify the expression \(\frac{1}{3} q(-12 q - 9)\), we need to distribute the \(\frac{1}{3} q\) term to both terms inside the parentheses. This involves multiplying \(\frac{1}{3} q\) by \(-12 q\) and \(\frac{1}{3} q\) by \(-9\).

We start with the expression

\[ \frac{1}{3} q(-12 q - 9). \]

To simplify, we distribute \(\frac{1}{3} q\) to both terms inside the parentheses:

\[ \frac{1}{3} q \cdot (-12 q) + \frac{1}{3} q \cdot (-9). \]

Calculating each term separately, we have:

1. For the first term: \[ \frac{1}{3} q \cdot (-12 q) = -4 q^2. \]

2. For the second term: \[ \frac{1}{3} q \cdot (-9) = -3 q. \]

Now, we combine the results from the two multiplications:

\[ -4 q^2 - 3 q. \]

Final Answer