Question

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

Explanation:

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

Multiply each term in the first binomial by each term in the trinomial:
\(2x \times (-3x^2) + 2x \times (-6x) + 2x \times (-4) + 1 \times (-3x^2) + 1 \times (-6x) + 1 \times (-4)\)

Step2: Perform the multiplications

Calculate each product:
\(2x \times (-3x^2) = -6x^3\)
\(2x \times (-6x) = -12x^2\)
\(2x \times (-4) = -8x\)
\(1 \times (-3x^2) = -3x^2\)
\(1 \times (-6x) = -6x\)
\(1 \times (-4) = -4\)

Step3: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms:
For \(x^2\) terms: \(-12x^2 - 3x^2 = -15x^2\)
For \(x\) terms: \(-8x - 6x = -14x\)
Now, put all the terms together: \(-6x^3 - 15x^2 - 14x - 4\)

Answer:

\(-6x^3 - 15x^2 - 14x - 4\)