Question

expand the expression to a polynomial in standard form: ((3x + 1)(2x^2 - 2x - 9))

Explanation:

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

Multiply \(3x\) by each term in \(2x^2 - 2x - 9\) and \(1\) by each term in \(2x^2 - 2x - 9\):
\(3x \times 2x^2 = 6x^3\), \(3x \times (-2x) = -6x^2\), \(3x \times (-9) = -27x\)
\(1 \times 2x^2 = 2x^2\), \(1 \times (-2x) = -2x\), \(1 \times (-9) = -9\)

Step2: Combine like terms

Now, combine the terms:
\(6x^3 - 6x^2 + 2x^2 - 27x - 2x - 9\)
Combine the \(x^2\) terms: \(-6x^2 + 2x^2 = -4x^2\)
Combine the \(x\) terms: \(-27x - 2x = -29x\)
So the polynomial becomes \(6x^3 - 4x^2 - 29x - 9\)

Answer:

\(6x^3 - 4x^2 - 29x - 9\)