To rewrite the algebraic expression $4(2x + 3)$ without parentheses using the distributive property, we will distribute the multiplication of $4$ across each term inside the parentheses.

Distributive Property

The distributive property states that for any numbers $a$, $b$, and $c$:

$a(b + c) = ab + ac$

Applying the Distributive Property

Given the expression:

$4(2x + 3)$

We distribute the $4$ across both $2x$ and $3$:

$4 \cdot 2x + 4 \cdot 3$

Simplifying the Expression

Now, perform the multiplication:

$4 \cdot 2x = 8x$

$4 \cdot 3 = 12$

So, the expression simplifies to:

$8x + 12$

Final Answer

The algebraic expression rewritten without parentheses using the distributive property is:

$8x + 12$

Would you like more details on any step or have any questions?

Follow-up Questions:

1. What happens if you distribute a negative number instead of a positive one?
2. How would the distributive property change if the expression inside the parentheses was a subtraction instead of addition?
3. Can the distributive property be used to factor an expression? How?
4. How can the distributive property help in solving equations?
5. Is the distributive property applicable in reverse, and how would you use it?

Tip: The distributive property is especially useful when you want to simplify expressions or solve equations with parentheses!