Expand the expression to a polynomial in standard form:
left parenthesis, x, minus, 3, right parenthesis, left parenthesis, minus, x, squared, minus, x, plus, 9, right parenthesis
(x−3)(−x
2
−x+9)

Let's expand the given expression \((x - 3)(-x^2 - x + 9)\) using the distributive property.

### Step 1: Apply the distributive property
We distribute each term in the first binomial \((x - 3)\) to each term in the second trinomial \((-x^2 - x + 9)\).

\[
(x - 3)(-x^2 - x + 9) = x(-x^2 - x + 9) - 3(-x^2 - x + 9)
\]

### Step 2: Distribute \(x\) to \((-x^2 - x + 9)\)

\[
x(-x^2 - x + 9) = x(-x^2) + x(-x) + x(9)
\]
\[
= -x^3 - x^2 + 9x
\]

### Step 3: Distribute \(-3\) to \((-x^2 - x + 9)\)

\[
-3(-x^2 - x + 9) = -3(-x^2) - 3(-x) - 3(9)
\]
\[
= 3x^2 + 3x - 27
\]

### Step 4: Combine the terms
Now, we add up the two results from the previous steps:

\[
-x^3 - x^2 + 9x + 3x^2 + 3x - 27
\]

Combine like terms:

\[
-x^3 + (-x^2 + 3x^2) + (9x + 3x) - 27
\]
\[
= -x^3 + 2x^2 + 12x - 27
\]

### Final Answer:
The expanded polynomial in standard form is:

\[
-x^3 + 2x^2 + 12x - 27
\]

Would you like further details or have any questions about this process?

Here are 5 related questions you might find helpful:
1. How do you identify like terms in a polynomial?
2. How do you apply the distributive property for expanding binomials?
3. What does it mean for a polynomial to be in standard form?
4. How can you factor a polynomial after expansion?
5. What is the difference between binomials and trinomials?

**Tip:** Always ensure that polynomials are arranged in decreasing order of their powers for standard form.

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

Learn how to expand the polynomial expression (x - 3)(-x^2 - x + 9) using the distributive property. This step-by-step solution explains how to distribute terms and combine like terms to get the final answer in standard form: -x^3 + 2x^2 + 12x - 27. Suitable for Grades 9-11 students.

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