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Simplifying expressions means making an expression easier to read and work with by reducing it to its simplest form. This process focuses on combining terms that are similar, which helps eliminate unnecessary components in a mathematical statement.

To simplify an expression effectively, you start by identifying the like terms. These are terms within the expression that have the same variables raised to identical powers. Once identified, like terms can be combined by performing arithmetic operations on their respective coefficients.

The goal is to make the expression as compact as possible without changing its value. In our exercise example, we simplified the expression from multiple terms down to just a single term:

• Original: 8y + y - 2y - 8y
• Simplified: -y

Coefficients are the numerical factors that multiply the variables in an expression. They tell you how many of that variable you have. For any variable term, the coefficient is the number sitting right in front of that variable.

If a variable appears without a number in front of it, the coefficient is assumed to be 1. This is because multiplying any number by one leaves the number unchanged, making it a perfect 'invisible' companion.

In the expression from our exercise, each term involving the variable 'y' has a coefficient:

• 8y (Coefficient: 8)
• y (Coefficient: 1)
• -2y (Coefficient: -2)
• -8y (Coefficient: -8)

Combining these coefficients, as shown in the step-by-step solution, helps us arrive at the simplified expression.

Like terms are crucial for simplifying algebraic expressions. They are terms that contain the same variables raised to the same power. This means they can be combined through addition or subtraction.

Understanding like terms allows you to simplify expressions by combining them, which reduces the complexity of an expression significantly. When evaluating expressions, identifying like terms quickly makes the simplification process smoother.

In our initial expression, all terms were like terms because they all involved the variable 'y':

• 8y, 1y, -2y, and -8y

Recognizing these terms as like terms allowed the unifying step of combining their coefficients, leading to a straightforward simplification.