How do you simplify the expression 4(2x + 1)?

To simplify the expression (4(2x + 1)), you can utilize the distributive property, which states that for any numbers (a), (b), and (c), the equation (a(b + c) = ab + ac) holds true.

Applying the distributive property to the given expression, you multiply (4) by both terms inside the parentheses:

1. First, multiply (4) by (2x):

[

4 \times 2x = 8x

]

2. Next, multiply (4) by (1):

[

4 \times 1 = 4

]

Now, combine both results:

[

8x + 4

]

Thus, the simplified expression is (8x + 4), which corresponds to the correct answer. This demonstrates how the distributive property works effectively to break down and simplify expressions involving parentheses in algebra.