https://file.aiquickdraw.com/mathbot/file/1727058003132vf0dblg1.jpg

The expression given in the image is:

\[
(x + 2)(x - 4)(5x - 6)
\]

To simplify this expression, we will expand the terms step by step.

### Step 1: Expand the first two terms \((x + 2)(x - 4)\)

\[
(x + 2)(x - 4) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8
\]

### Step 2: Multiply the result by the third term \((5x - 6)\)

\[
(x^2 - 2x - 8)(5x - 6) = x^2(5x - 6) - 2x(5x - 6) - 8(5x - 6)
\]

Now, distribute each term:

\[
= x^2(5x) - x^2(6) - 2x(5x) + 2x(6) - 8(5x) + 8(6)
\]

\[
= 5x^3 - 6x^2 - 10x^2 + 12x - 40x + 48
\]

### Step 3: Combine like terms

\[
5x^3 - (6x^2 + 10x^2) + (12x - 40x) + 48 = 5x^3 - 16x^2 - 28x + 48
\]

Thus, the simplified polynomial is:

\[
5x^3 - 16x^2 - 28x + 48
\]

Would you like more details on any of these steps?

### Related Questions:
1. How do you expand binomials using the distributive property?
2. How does the degree of a polynomial affect its graph?
3. What are the different ways to factor polynomials?
4. What are common methods to simplify complex polynomials?
5. Can the result \(5x^3 - 16x^2 - 28x + 48\) be factored further?

### Tip:
When expanding polynomials, ensure you carefully distribute each term and then combine like terms to avoid mistakes.

Learn how to expand and simplify the polynomial expression (x + 2)(x - 4)(5x - 6). This problem involves the use of algebraic concepts such as the distributive property and polynomial expansion. Suitable for students in Grades 9-11.

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