91Ó°ÊÓ

When distributing negatives, we need to carefully apply the negative sign to every term inside the parentheses. This is crucial for simplifying algebraic expressions accurately. In the given exercise, the expression starts as:
6 + 3p - (2p + 1) - (2p + 9).

You need to 'distribute' the negative sign in front of each parentheses to all the terms within:
- (2p + 1) becomes -2p - 1
- (2p + 9) becomes -2p - 9

So after distributing, the expression becomes:
6 + 3p - 2p - 1 - 2p - 9.

Each distributed term changes its sign, ensuring we set up the problem correctly for further simplification. This step must be done cautiously to avoid errors that could lead to incorrect final results.

Simplifying algebraic expressions involves combining and reducing terms to make the expression as simple as possible. After distributing the negatives in our exercise, we have:
6 + 3p - 2p - 1 - 2p - 9.

To simplify this expression, we need to combine all the similar terms. For example:

• Combine all the constant terms (numbers without variables).
• Combine all the terms with the variable p.

This process is a key step in simplifying algebraic expressions because it helps us reduce the complexity and make the expression easier to understand and work with.

Combining constants and coefficients is an essential part of simplifying algebraic expressions. Constants are number terms without variables, while coefficients are the numbers in front of the variables. In the exercise, we have constants (6, -1, and -9) and p-terms (3p, -2p, -2p).

First, combine the constants:
6 - 1 - 9 = -4.

Then, combine the coefficients of p:
3p - 2p - 2p = 3p - 4p = -4p.

So, putting it all together, the final simplified expression is:
-4p - 4.

By methodically combining like terms and coefficients, we achieve a cleaner, more manageable expression that accurately represents the original problem.