https://file.aiquickdraw.com/mathbot/file/1726336771012ya4rfwkm.jpg

The expression in the image is:

\[
(2x - 1)(x + 5)(3x - 2)
\]

To simplify this, we need to multiply the three binomials together step-by-step.

### Step 1: Multiply the first two binomials
First, multiply \((2x - 1)(x + 5)\).

Using the distributive property (FOIL method):
\[
(2x - 1)(x + 5) = 2x(x + 5) - 1(x + 5)
\]
\[
= 2x^2 + 10x - x - 5
\]
\[
= 2x^2 + 9x - 5
\]

### Step 2: Multiply the result by the third binomial
Now, multiply \((2x^2 + 9x - 5)\) by \((3x - 2)\).

\[
(2x^2 + 9x - 5)(3x - 2)
\]

Distribute each term from the first polynomial to the second polynomial:
\[
= 2x^2(3x - 2) + 9x(3x - 2) - 5(3x - 2)
\]
Multiply term by term:
\[
= 6x^3 - 4x^2 + 27x^2 - 18x - 15x + 10
\]
Now, combine like terms:
\[
= 6x^3 + (27x^2 - 4x^2) + (-18x - 15x) + 10
\]
\[
= 6x^3 + 23x^2 - 33x + 10
\]

### Final Answer:
\[
6x^3 + 23x^2 - 33x + 10
\]

This is the fully simplified form of the expression.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you apply the distributive property to binomials?
2. What is the FOIL method and how does it work for multiplying two binomials?
3. How do you multiply polynomials with more than two terms?
4. What is the degree of a polynomial, and what does it represent?
5. How can you factor the resulting polynomial?

**Tip:** When multiplying polynomials, organize your terms carefully to avoid missing any combinations.

Learn how to simplify and multiply the polynomial expression (2x - 1)(x + 5)(3x - 2) using the distributive property and FOIL method. This solution includes a detailed step-by-step breakdown for high school students. Perfect for Grades 10-12.

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