To express $(x+2)(2x^2 - x - 9)$ in standard form, we expand the expression using the distributive property.

Step 1: Expand the expression

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

Step 2: Distribute $x$ and $2$

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

Step 3: Combine the results

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

Step 4: Combine like terms

$2x^3 + (-x^2 + 4x^2) + (-9x - 2x) - 18$ $2x^3 + 3x^2 - 11x - 18$

Final Answer:

$\boxed{2x^3 + 3x^2 - 11x - 18}$

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Related Questions:

1. How do you expand other binomial and polynomial expressions?
2. How can you verify the result by factoring the standard form back?
3. What is the significance of the standard form in polynomial equations?
4. How would the standard form change if the terms of the polynomial were rearranged initially?
5. What methods can you use to quickly identify errors in polynomial expansion?

Tip:

When expanding polynomials, write each term systematically to avoid missing or miscalculating terms!