Expand the expression to a polynomial in standard form:

left parenthesis, 3, x, minus, 1, right parenthesis, left parenthesis, 3, x, squared, plus, 4, x, minus, 5, right parenthesis

(3*x*−1)(3*x*2+4*x*−5)

To expand the expression \((3x - 1)(3x^2 + 4x - 5)\), we'll distribute each term in the first binomial across the second trinomial.

### Step 1: Distribute \(3x\) across \(3x^2 + 4x - 5\):
\[
3x \cdot 3x^2 = 9x^3
\]
\[
3x \cdot 4x = 12x^2
\]
\[
3x \cdot (-5) = -15x
\]

### Step 2: Distribute \(-1\) across \(3x^2 + 4x - 5\):
\[
-1 \cdot 3x^2 = -3x^2
\]
\[
-1 \cdot 4x = -4x
\]
\[
-1 \cdot (-5) = 5
\]

### Step 3: Combine all the terms:
\[
9x^3 + 12x^2 - 15x - 3x^2 - 4x + 5
\]

### Step 4: Combine like terms:
\[
9x^3 + (12x^2 - 3x^2) + (-15x - 4x) + 5
\]
\[
9x^3 + 9x^2 - 19x + 5
\]

### Final Answer:
The expanded polynomial in standard form is:
\[
\boxed{9x^3 + 9x^2 - 19x + 5}
\]

Would you like any details or have questions on this solution?

Here are some related questions:
1. How do you factor the polynomial \(9x^3 + 9x^2 - 19x + 5\)?
2. What is the degree of the polynomial \(9x^3 + 9x^2 - 19x + 5\)?
3. How do you expand the expression \((x + 2)(2x^2 - 3x + 1)\)?
4. What happens when you multiply a binomial by a trinomial?
5. How can you use synthetic division on the polynomial \(9x^3 + 9x^2 - 19x + 5\)?

**Tip:** When distributing, keep track of signs carefully to avoid mistakes when combining like terms.

Learn how to expand the expression (3x - 1)(3x^2 + 4x - 5) step-by-step with detailed explanations and examples. This problem involves polynomials and the distributive property, suitable for high school students.

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