Question

question
simplify: (\frac{-9p^3 + 21p^2}{3})
answer attempt 1 out of 3

Explanation:

Step1: Factor out common terms in numerator

First, we factor out the greatest common factor (GCF) from the numerator \(-9p^{3}+21p^{2}\). The GCF of \(-9p^{3}\) and \(21p^{2}\) is \(3p^{2}\). So we can rewrite the numerator as:
\(-9p^{3}+21p^{2}=3p^{2}(-3p + 7)\)
The original expression \(\frac{-9p^{3}+21p^{2}}{3}\) now becomes \(\frac{3p^{2}(-3p + 7)}{3}\)

Step2: Simplify the fraction

We can cancel out the common factor of \(3\) in the numerator and the denominator. So we have:
\(\frac{3p^{2}(-3p + 7)}{3}=p^{2}(-3p + 7)\)
We can also distribute the \(p^{2}\) (though it's also acceptable to leave it factored) to get \(-3p^{3}+7p^{2}\)

Answer:

\(-3p^{3}+7p^{2}\) (or \(p^{2}(-3p + 7)\))