Question

find the product. simplify your answer. \\(3p^2(p^2 - 3p)\\)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b - c)=ab - ac\), here \(a = 3p^{2}\), \(b=p^{2}\), \(c = 3p\). So we have \(3p^{2}\times p^{2}-3p^{2}\times3p\).

Step2: Use exponent rule \(a^{m}\times a^{n}=a^{m + n}\)

For the first term \(3p^{2}\times p^{2}\), according to the rule \(a^{m}\times a^{n}=a^{m + n}\), we get \(3p^{2+2}=3p^{4}\). For the second term \(3p^{2}\times3p\), we have \(3\times3\times p^{2+1}=9p^{3}\).

Step3: Combine the terms

Combining the two terms, we get \(3p^{4}-9p^{3}\).

Answer:

\(3p^{4}-9p^{3}\)