Question

find the product. simplify your answer.
(2h - 1)(-3h² - 4h - 3)

Explanation:

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

Multiply \(2h\) by each term in \(-3h^2 - 4h - 3\) and \(-1\) by each term in \(-3h^2 - 4h - 3\).
\(2h\times(-3h^2)+2h\times(-4h)+2h\times(-3)+(-1)\times(-3h^2)+(-1)\times(-4h)+(-1)\times(-3)\)
\(=-6h^3 - 8h^2 - 6h + 3h^2 + 4h + 3\)

Step2: Combine like terms

Combine the \(h^2\) terms and the \(h\) terms.
For \(h^2\): \(-8h^2 + 3h^2=-5h^2\)
For \(h\): \(-6h + 4h=-2h\)
So the expression becomes \(-6h^3 - 5h^2 - 2h + 3\)

Answer:

\(-6h^3 - 5h^2 - 2h + 3\)