Question

multiply.
(6v + 2)(7v² - 4v - 3)
simplify your answer.

Explanation:

Step1: Apply distributive property (FOIL for binomial and trinomial)

Multiply \(6v\) by each term in \(7v^2 - 4v - 3\) and \(2\) by each term in \(7v^2 - 4v - 3\).
\(6v\times7v^2 = 42v^3\), \(6v\times(-4v)= -24v^2\), \(6v\times(-3)= -18v\)
\(2\times7v^2 = 14v^2\), \(2\times(-4v)= -8v\), \(2\times(-3)= -6\)

Step2: Combine like terms

Combine the \(v^2\) terms: \(-24v^2 + 14v^2 = -10v^2\)
Combine the \(v\) terms: \(-18v - 8v = -26v\)

Step3: Write the final polynomial

Combine all terms: \(42v^3 - 10v^2 - 26v - 6\)

Answer:

\(42v^3 - 10v^2 - 26v - 6\)