Let's break down and simplify the given expression:

\[
[5 \times (x + 4)] + 2x \times [2x - 1] + 6 + 4
\]

### Step 1: Expand and simplify
1. **Expand the first term:**  
\[
5 \times (x + 4) = 5x + 20
\]

2. **Expand the second term:**  
\[
2x \times (2x - 1) = 2x \times 2x - 2x = 4x^2 - 2x
\]

3. Combine the constants:  
\[
6 + 4 = 10
\]

### Step 2: Rewrite the full expression
Now, substitute the expanded terms back into the original equation:
\[
5x + 20 + 4x^2 - 2x + 10
\]

### Step 3: Combine like terms
\[
4x^2 + (5x - 2x) + (20 + 10)
\]
\[
4x^2 + 3x + 30
\]

### Final expression:
\[
4x^2 + 3x + 30
\]

Let me know if you'd like a detailed explanation of any step!

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Here are five related questions for practice:
1. Simplify \( 3(x + 2) + 4x(2x - 3) \).
2. Expand and combine terms: \( 7(x - 5) + 3(2x + 4) \).
3. Solve for \( x \) in \( 4x^2 + 3x + 30 = 0 \).
4. Factor the quadratic \( 4x^2 + 3x - 30 \).
5. Simplify \( 2x(3x + 5) + 4(2x - 1) \).

**Tip:** Always combine like terms after expanding to simplify expressions easily.

The query submitted by the user: [5×(×+4)]+2×[2×-1]+6+4

Learn how to simplify the algebraic expression 5(x + 4) + 2x(2x - 1) + 6 + 4 step-by-step. This problem involves polynomial expansion, using the distributive property, and combining like terms. Suitable for students in Grades 8-10.

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