Question

find the product. simplify your \\(4r(2r^2 - 6)\\)

Explanation:

Step1: Apply distributive property

Use the distributive property \( a(b - c)=ab - ac \), here \( a = 4r \), \( b=2r^{2} \), \( c = 6 \). So we get \( 4r\times2r^{2}-4r\times6 \).

Step2: Simplify each term

For the first term, \( 4r\times2r^{2}=8r^{3} \) (using \( a^{m}\times a^{n}=a^{m + n} \) and \( 4\times2 = 8 \)). For the second term, \( 4r\times6 = 24r \). So the expression becomes \( 8r^{3}-24r \).

Answer:

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