Let's simplify the expression \((4a+2)(6a - a + 2)\).

1. First, simplify the second factor:

\[
6a - a + 2 = 5a + 2
\]

So, the expression becomes:

\[
(4a + 2)(5a + 2)
\]

2. Now, apply the distributive property (also known as the FOIL method for binomials):

\[
(4a + 2)(5a + 2) = (4a)(5a) + (4a)(2) + (2)(5a) + (2)(2)
\]

3. Simplify each term:

\[
(4a)(5a) = 20a^2
\]
\[
(4a)(2) = 8a
\]
\[
(2)(5a) = 10a
\]
\[
(2)(2) = 4
\]

4. Combine like terms:

\[
20a^2 + 8a + 10a + 4 = 20a^2 + 18a + 4
\]

So, the simplified expression is:

\[
20a^2 + 18a + 4
\]

Would you like further details or have any questions? 

Here are 5 related questions to explore further:
1. How would you factor the expression \(20a^2 + 18a + 4\)?
2. What happens if you substitute a value for \(a\) in the expression?
3. How does the distributive property apply to larger polynomials?
4. Can you simplify the expression using a different method, like completing the square?
5. How can this binomial expansion be useful in solving equations?

**Tip:** When expanding binomials, always remember to distribute every term in the first binomial to every term in the second!

Explore how to simplify the algebraic expression (4a+2)(6a - a + 2) by applying the distributive property. Follow a step-by-step solution to expand and combine like terms, resulting in 20a^2 + 18a + 4. Suitable for students in Grades 8-10 learning about binomial expansion and algebra.

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