Question

find the product.
-3v(3 - 4v + 3v²)

Explanation:

Step1: Distribute -3v to each term

Using the distributive property \(a(b + c + d)=ab+ac+ad\), we have:
\(-3v\times3 + (-3v)\times(-4v)+(-3v)\times(3v^{2})\)

Step2: Simplify each term

• For the first term: \(-3v\times3=-9v\)
• For the second term: \((-3v)\times(-4v)=12v^{2}\) (since multiplying two negative numbers gives a positive, and \(v\times v = v^{2}\))
• For the third term: \((-3v)\times(3v^{2})=-9v^{3}\) (multiplying the coefficients \(-3\times3 = -9\), and \(v\times v^{2}=v^{3}\))

Step3: Combine the simplified terms

Putting them together, we get \(-9v + 12v^{2}-9v^{3}\), which can be rewritten in standard form as \(-9v^{3}+12v^{2}-9v\)

Answer:

\(-9v^{3}+12v^{2}-9v\)