Question

question
expand the expression to a polynomial in standard form:
(4x - 1)(-3x² - 2x - 6)

Explanation:

Step1: Apply the distributive property (FOIL for polynomials)

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 term

• For \(4x\times(-3x^{2})\): Using the rule \(a^{m}\times a^{n}=a^{m + n}\), we get \(-12x^{3}\).
• For \(4x\times(-2x)\): We get \(-8x^{2}\).
• For \(4x\times(-6)\): We get \(-24x\).
• For \((-1)\times(-3x^{2})\): We get \(3x^{2}\).
• For \((-1)\times(-2x)\): We get \(2x\).
• For \((-1)\times(-6)\): We get \(6\).

Step3: Combine like terms

Combine the \(x^{2}\) terms and the \(x\) terms:

• \(x^{2}\) terms: \(-8x^{2}+3x^{2}=-5x^{2}\)
• \(x\) terms: \(-24x + 2x=-22x\)

Putting it all together, we have \(-12x^{3}-5x^{2}-22x + 6\).

Answer:

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