Question

find the product. simplify yo -2v(-v² - 6)

Explanation:

Step1: Apply distributive property

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

Step2: Simplify each term

For the first term, \(-2v\times(-v^{2})\), using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\) and the rule of multiplying two negative numbers (which gives a positive number), we get \(2v^{1 + 2}=2v^{3}\).
For the second term, \((-2v)\times(-6)\), multiplying two negative numbers gives a positive number, so we get \(12v\).

Step3: Combine the terms

Combining the two simplified terms, we get \(2v^{3}+12v\).

Answer:

\(2v^{3}+12v\)