Question

find the product. simplify your answer.
$4q(-2q^{3}-6)$

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\) (here \(a = 4q\), \(b=- 2q^{3}\), \(c = - 6\)). So we have \(4q\times(-2q^{3})+4q\times(-6)\).

Step2: Multiply the coefficients and add exponents for like bases

For \(4q\times(-2q^{3})\), the coefficient is \(4\times(-2)=-8\), and for the variable part \(q\times q^{3}=q^{1 + 3}=q^{4}\) (using the rule \(a^{m}\times a^{n}=a^{m + n}\)). For \(4q\times(-6)\), we get \(-24q\).
So combining these two results, we have \(-8q^{4}-24q\).

Answer:

\(-8q^{4}-24q\)