Question

find the product. simplify your answer
4q(-2q² - 6)

Explanation:

Step1: Apply distributive property

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

Step2: Multiply the coefficients and add exponents for variables

For the first term \(4q\times(-2q^{2})\), multiply the coefficients \(4\times(-2)=-8\) and add the exponents of \(q\) (using \(a^{m}\times a^{n}=a^{m + n}\)), so \(q\times q^{2}=q^{1+2}=q^{3}\), thus the first term is \(-8q^{3}\). For the second term \(4q\times(-6)\), multiply \(4\times(-6)=-24\) and keep the variable \(q\), so the second term is \(-24q\).

Step3: Combine the terms

Combining the two terms we get \(-8q^{3}-24q\).

Answer:

\(-8q^{3}-24q\)