To multiply algebraic expressions, you can follow these simple steps:

1. Find the Terms: Look at each part of the expressions you are working with. For example, in $3x^2$ and $4xy$, the terms are $3x^2$ and $4xy$.

2. Use the Distributive Property: This means you'll multiply each part of the first expression by each part of the second expression. You can use the FOIL method if you are working with two parts (called binomials).

3. Combine Like Terms: After you finish multiplying, look for any terms that are similar and group them together to make it simpler.

4. Show the Final Result: Clearly write down what you got after doing the multiplication.

For example, when you multiply $(2x + 3)(x + 4)$, you get $2x^2 + 11x + 12$.

By following these steps, anyone can successfully multiply algebraic expressions!