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!