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The distributive property is a fundamental concept in algebra. It helps us to handle expressions with parentheses, especially when they involve subtraction or negative signs. When you see a negative sign in front of a parenthesis, it's crucial to distribute that sign to each term inside. For our example, the expression

• (2y + 5) - (y + 8)

can be tricky because of the subtraction.
Think of the negative sign as "negative 1" multiplying the expression inside the parentheses. Instead of just ignoring the parentheses, you need to subtract each term individually:

• This results in -(y + 8) becoming -y - 8.

Now, write it out:

• 2y + 5 - y - 8

This step is important because it sets the stage for proper combination and simplification.

Combining like terms is about simplifying expressions by adding or subtracting terms that have the same variable. In algebra, 'like terms' are terms whose variables and their exponents match completely.
Look at our expression:

• 2y + 5 - y - 8

Identify the terms with the variable 'y':

• 2y and -y

Combine these by adding or subtracting their coefficients (the numbers in front of the variables). In this case:

• 2y - y = y

Now, do the same for the constant terms:

• 5 and -8
• 5 - 8 = -3

Combine everything together to get the simplified form of the expression:

• y - 3

This step helps you see the expression in its simplest form.

Simplification is the process of rewriting an expression in a cleaner and more concise form. After distributing and combining like terms, simplifying is often one of the final steps in solving or rewriting algebraic expressions. It helps to evaluate and understand the expression better.
With our example, the expression has been reduced from:

• 2y + 5 - y - 8

to

• y - 3

This means there are no more like terms to combine or parentheses to address. The expression is now fully simplified.
Remember, a simplified expression is easier to work with in further calculations or when solving equations. It’s always a good idea to ensure that your final answer is in its simplest form, free from parentheses and unnecessary complexity.