Question

find the product. simplify your answer.
(4s - 2)(4s² - s + 3)

Explanation:

Step1: Apply Distributive Property

Multiply each term in the first polynomial by each term in the second polynomial:
\(4s(4s^2 - s + 3) - 2(4s^2 - s + 3)\)

Step2: Distribute Further

For \(4s(4s^2 - s + 3)\):
\(4s \times 4s^2 = 16s^3\), \(4s \times (-s) = -4s^2\), \(4s \times 3 = 12s\)
For \(-2(4s^2 - s + 3)\):
\(-2 \times 4s^2 = -8s^2\), \(-2 \times (-s) = 2s\), \(-2 \times 3 = -6\)

Step3: Combine Like Terms

Combine the \(s^2\) terms: \(-4s^2 - 8s^2 = -12s^2\)
Combine the \(s\) terms: \(12s + 2s = 14s\)

Step4: Write the Final Polynomial

Put all terms together: \(16s^3 - 12s^2 + 14s - 6\)

Answer:

\(16s^3 - 12s^2 + 14s - 6\)