Question

Find the product. $$3 q\left(q^{3}-5 q^{2}+6\right)$$

Short answer

The simplified form of the expression \(3q(q^{3}-5q^{2}+6)\) is \(3q^{4} - 15q^{3} + 18q\).

Step-by-step solution

Distribute \(3q\) Across the Terms in the Parentheses

Utilize the distributive property of multiplication to distribute \(3q\) to each term in the parentheses. The distributive property states that \(a(b + c) = ab + ac\). Hence, \(3q \cdot q^{3}\) goes to \(3q^{4}\), \(3q \cdot (-5q^{2})\) results in \(-15q^{3}\), and finally, \(3q \cdot 6\) becomes \(+18q\).

Write Down the Complete Expression

Incorporate all the resulting terms from the previous step into the final expression. Doing this gives us \(3q^{4} - 15q^{3} + 18q\).