Question

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

Explanation:

Step1: Apply distributive property (FOIL for trinomial)

Multiply \(-2x\) by each term in \((x^2 + 9x + 3)\) and \(-1\) by each term in \((x^2 + 9x + 3)\):
\(-2x \cdot x^2 + (-2x) \cdot 9x + (-2x) \cdot 3 + (-1) \cdot x^2 + (-1) \cdot 9x + (-1) \cdot 3\)

Step2: Simplify each term

\(-2x^3 - 18x^2 - 6x - x^2 - 9x - 3\)

Step3: Combine like terms

Combine the \(x^2\) terms: \(-18x^2 - x^2 = -19x^2\)
Combine the \(x\) terms: \(-6x - 9x = -15x\)
So the expression becomes \(-2x^3 - 19x^2 - 15x - 3\)

Answer:

\(-2x^3 - 19x^2 - 15x - 3\)