Question

question
expand the expression to a polynomial in standard form:
$(4x - 1)(-3x^2 - 2x - 6)$

Explanation:

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

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

Step2: Simplify each product

\(-12x^3 - 8x^2 - 24x + 3x^2 + 2x + 6\)

Step3: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms.
\(-12x^3 + (-8x^2 + 3x^2) + (-24x + 2x) + 6\)
\(-12x^3 - 5x^2 - 22x + 6\)

Answer:

\(-12x^3 - 5x^2 - 22x + 6\)