Let's simplify the expression step-by-step:

The expression is:

\[
\frac{(4x + 2) \times (5x + 4)}{2}
\]

### Step 1: Expand the Numerator

First, let's expand the product \((4x + 2) \times (5x + 4)\) in the numerator using the distributive property (FOIL method):

\[
(4x + 2)(5x + 4) = 4x \cdot 5x + 4x \cdot 4 + 2 \cdot 5x + 2 \cdot 4
\]

\[
= 20x^2 + 16x + 10x + 8
\]

\[
= 20x^2 + 26x + 8
\]

### Step 2: Divide by 2

Now, divide the expanded expression by 2:

\[
\frac{20x^2 + 26x + 8}{2}
\]

To simplify this, divide each term in the numerator by 2:

\[
= \frac{20x^2}{2} + \frac{26x}{2} + \frac{8}{2}
\]

\[
= 10x^2 + 13x + 4
\]

### Final Simplified Expression

The simplified form of the given expression is:

\[
10x^2 + 13x + 4
\]

### Would you like more details or have any further questions?

Here are some related questions to explore:

1. How do you expand and simplify expressions using the distributive property?
2. What is the process for dividing a polynomial by a constant?
3. How can you factor a quadratic expression like \(10x^2 + 13x + 4\)?
4. How do you identify like terms when simplifying algebraic expressions?
5. What are some common techniques for simplifying algebraic fractions?

**Tip:** When working with fractions in algebra, always simplify the numerator and denominator separately before performing division to ensure accuracy.

Learn how to simplify the expression (4x+2) × (5x+4) / 2 step-by-step. Understand the distributive property in algebra and how to divide polynomials. Suitable for students in Grades 7-9.

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