https://file.aiquickdraw.com/mathbot/file/1725482100109d9yci6ee.jpg

It seems that there was a small issue with the OCR text extraction, particularly with some symbols. However, based on the image, the expression to expand and simplify is:

\[
(2x - 1)(x - 5)(x + 6)
\]

Let's solve this step by step.

### Step 1: Expand the first two binomials

First, expand \((2x - 1)(x - 5)\):

\[
(2x - 1)(x - 5) = 2x(x - 5) - 1(x - 5)
\]

\[
= 2x^2 - 10x - x + 5 = 2x^2 - 11x + 5
\]

### Step 2: Multiply the result by the third binomial

Now, multiply \((2x^2 - 11x + 5)\) by \((x + 6)\):

\[
(2x^2 - 11x + 5)(x + 6) = (2x^2)(x + 6) - (11x)(x + 6) + (5)(x + 6)
\]

Expanding each term:

\[
= 2x^3 + 12x^2 - 11x^2 - 66x + 5x + 30
\]

### Step 3: Combine like terms

Now, combine the like terms:

\[
= 2x^3 + (12x^2 - 11x^2) + (-66x + 5x) + 30
\]
\[
= 2x^3 + x^2 - 61x + 30
\]

### Final Answer:
The fully expanded and simplified expression is:

\[
2x^3 + x^2 - 61x + 30
\]

Do you want further details on any specific step? Here are some related questions:

1. How do you perform binomial expansion for quadratic expressions?
2. Why is it important to combine like terms in polynomial expressions?
3. Can you expand and simplify other similar polynomial products?
4. What happens if you miss a step in polynomial expansion?
5. How do the coefficients in the final polynomial expression relate to the original factors?

**Tip:** Always double-check your expanded terms before combining them to avoid mistakes!

Expand and fully simplify (2x - 1)(x - 5)(x + 6)

Learn how to expand and simplify the polynomial expression (2x - 1)(x - 5)(x + 6) in this detailed step-by-step solution. This problem covers essential algebraic concepts like multiplying binomials and combining like terms, suitable for students in Grades 9-11.

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