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When working with algebraic expressions, it's important to distribute values inside the parentheses to simplify the equation. Distributing means multiplying the term outside the parentheses by each term inside the parentheses. For example, in the expression: $$3(w+3)$$, we distribute the 3 to both **w** and 3, resulting in:

\(3w + 9\)

This step makes it easier to combine and simplify terms later on. Always remember, the distributive property allows you to multiply a single term by each term inside the parentheses. This is commonly written as: \( a(b+c) = ab + ac \). Distributing expressions might look intimidating at first but it’s essential for simplifying algebraic expressions. Practice this technique to become more comfortable with it.

In algebra, clearing parentheses means removing the parentheses by applying the distributive property or by simplifying the terms inside them. Clearing parentheses simplifies the expression and readies it for combining like terms. For example, in the expression:

\( 3w + 9 - (4w + y) - 3y \)

We need to distribute the negative sign across the terms in the second set of parentheses:

\( -(4w + y) = -4w - y \)

When you remove the parentheses, your expression will become:

\( 3w + 9 - 4w - y - 3y \)

Clearing parentheses can seem tricky but if you take it step by step, it gets easier. Remember to always keep an eye on the signs (positive/negative) as they can change when you distribute across the parentheses.

Simplifying algebraic expressions involves combining like terms to make the expression as simple as possible. Like terms are terms with the same variables raised to the same power. For instance, in the expression:

\( 3w + 9 - 4w - y - 3y \)

You need to identify and combine the like terms. Starting with the terms involving **w**:

\( 3w - 4w = -w \)

Then, combining the **y** terms:

\( -y - 3y = -4y \)

Lastly, keep the constant term 9 as it is. Thus, the simplified expression becomes:

\( -w + 9 - 4y \)

Simplifying algebraic expressions helps in solving equations faster and understanding the relationship between different terms. Always combine like terms wherever possible for easier calculation and to simplify your workload.