Question

Use the distributive property to rewrite the expression.
negative four thirds left parenthesis 6 y plus 9 z right parenthesis
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Part 1
negative four thirds left parenthesis 6 y plus 9 z right parenthesis
equals
  
enter your response hereyminus
  
enter your response herez
​(Simplify your​ answer.)

Answer 1

To rewrite the expression \(-\frac{4}{3}(6y + 9z)\) using the distributive property, we need to distribute \(-\frac{4}{3}\) to both terms inside the parentheses.

1. Distributing \(-\frac{4}{3}\) to \(6y\):
\[
-\frac{4}{3} \cdot 6y = -\frac{24}{3}y = -8y
\]

2. Distributing \(-\frac{4}{3}\) to \(9z\):
\[
-\frac{4}{3} \cdot 9z = -\frac{36}{3}z = -12z
\]

Now, combine the two results:
\[
-\frac{4}{3}(6y + 9z) = -8y - 12z
\]

So, the expression simplifies to:
\[
-8y - 12z
\]

Thus, you can fill in the response as follows:
- The first blank is: \(8\)
- The second blank is: \(12\)

Final answer:
\(-\frac{4}{3}(6y + 9z) = -8y - 12z\)