Question

multiply. write your answer in simplest form.
\frac{5}{7} \cdot (12r^3 - 8r^2)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a\cdot(b - c)=a\cdot b - a\cdot c\) here. So, \(\frac{5}{7}\cdot(12r^{3}-8r^{2})=\frac{5}{7}\cdot12r^{3}-\frac{5}{7}\cdot8r^{2}\)

Step2: Calculate each term

For the first term: \(\frac{5}{7}\cdot12r^{3}=\frac{60}{7}r^{3}\)
For the second term: \(\frac{5}{7}\cdot8r^{2}=\frac{40}{7}r^{2}\)
So the expression becomes \(\frac{60}{7}r^{3}-\frac{40}{7}r^{2}\)

Answer:

\(\frac{60}{7}r^{3}-\frac{40}{7}r^{2}\)