Question

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

Explanation:

Step1: Distribute $-x$ to each term

$-x \cdot x^2 + (-x) \cdot 9x + (-x) \cdot (-2) = -x^3 -9x^2 +2x$

Step2: Distribute $2$ to each term

$2 \cdot x^2 + 2 \cdot 9x + 2 \cdot (-2) = 2x^2 +18x -4$

Step3: Combine the two results

$(-x^3 -9x^2 +2x) + (2x^2 +18x -4)$

Step4: Combine like terms

$-x^3 + (-9x^2+2x^2) + (2x+18x) -4 = -x^3 -7x^2 +20x -4$

Answer:

$-x^3 -7x^2 +20x -4$