Question

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

Explanation:

Step1: Distribute -2x

Multiply -2x by each term in \(x^2 + 9x + 3\):
\(-2x \cdot x^2 = -2x^3\), \(-2x \cdot 9x = -18x^2\), \(-2x \cdot 3 = -6x\).

Step2: Distribute -1

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

Step3: Combine like terms

Combine the results from Step1 and Step2:
\(-2x^3 - 18x^2 - 6x - x^2 - 9x - 3\)
Combine \( -18x^2 - x^2 = -19x^2 \) and \( -6x - 9x = -15x \).

Answer:

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