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

Explanation:

Step1: Use distributive property

$(-x + 2)(x^{2}+9x - 2)=-x(x^{2}+9x - 2)+2(x^{2}+9x - 2)$

Step2: Distribute -x

$-x(x^{2}+9x - 2)=-x\cdot x^{2}-x\cdot9x+x\cdot2=-x^{3}-9x^{2}+2x$

Step3: Distribute 2

$2(x^{2}+9x - 2)=2x^{2}+18x - 4$

Step4: Combine like - terms

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

Answer:

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