expand the expression to a polynomial in standard form: (x - 9)(x² + x + 2)

Explanation:

Step1: Use distributive property

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

Step2: Expand each part

For (x(x^{2}+x + 2)): $$x\cdot x^{2}+x\cdot x+x\cdot2=x^{3}+x^{2}+2x$$ For (-9(x^{2}+x + 2)): $$-9\cdot x^{2}-9\cdot x-9\cdot2=-9x^{2}-9x - 18$$

Step3: Combine like - terms

$$(x^{3}+x^{2}+2x)+(-9x^{2}-9x - 18)=x^{3}+(x^{2}-9x^{2})+(2x-9x)-18$$ $$=x^{3}-8x^{2}-7x - 18$$

Answer:

(x^{3}-8x^{2}-7x - 18)