To simplify the expression $3x(x + 4)$, you apply the distributive property (also known as the distributive law of multiplication over addition).

Step-by-Step Solution:

1. Distribute the $3x$ to both terms inside the parentheses: $3x(x + 4) = 3x \cdot x + 3x \cdot 4$

2. Simplify each term: $3x \cdot x = 3x^2$ $3x \cdot 4 = 12x$

Final Result:

$3x(x + 4) = 3x^2 + 12x$

Let me know if you'd like a deeper explanation or have any questions!

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Related Questions:

1. How would you factor the expression $3x^2 + 12x$?
2. What is the distributive property, and how is it used in algebra?
3. What are other common ways to simplify expressions like $2a(a + 5)$?
4. How can you apply this method to quadratic expressions?
5. What is the difference between the distributive property and combining like terms?

Tip: Remember, when multiplying terms in parentheses, you always multiply each term inside by the term outside the parentheses!