How to Simplify an Expression

Simplifying algebraic expressions is a fundamental skill in high school mathematics. It involves reducing the expression to its simplest form by combining like terms, applying the order of operations, and performing various algebraic operations. In this article, we'll explore the step-by-step process of simplifying expressions to help you master this important concept.

Identify Like Terms

The first step in simplifying an expression is to identify the like terms. Like terms are variables or constants that have the same variable(s) and exponent(s). For example, in the expression 3x^2 + 5y - 2x^2 + 4y, the like terms are 3x^2 and -2x^2, as well as 5y and 4y.

Combine Like Terms

Once you've identified the like terms, you can combine them by adding or subtracting their coefficients. In the example above, you would combine the x^2 terms by adding their coefficients: 3x^2 - 2x^2 = x^2. Similarly, you would combine the y terms by adding their coefficients: 5y + 4y = 9y.

The simplified expression would then be x^2 + 9y.

Apply the Order of Operations

When simplifying an expression, it's important to follow the correct order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

1. Parentheses: Evaluate any expressions inside parentheses, brackets, or other grouping symbols first.
2. Exponents: Simplify any exponents or roots.
3. Multiplication and Division: Perform multiplication and division from left to right.
4. Addition and Subtraction: Perform addition and subtraction from left to right.

By following the order of operations, you can ensure that you arrive at the correct simplified expression.

Examples

Let's go through a few examples to solidify your understanding of simplifying expressions:

1. Simplify the expression 2(x + 3) - 4x.

2. Evaluate the expression inside the parentheses: x + 3.

3. Multiply the result by 2: 2(x + 3) = 2x + 6.

4. Subtract 4x: 2x + 6 - 4x = -2x + 6.

5. Simplify the expression 5x^2 - 3x + 2x^2 + 4x - x^2.

6. Identify the like terms: 5x^2, 2x^2, and -x^2 are like terms; -3x and 4x are like terms.

7. Combine the like terms: 5x^2 + 2x^2 - x^2 = 6x^2, and -3x + 4x = x.

8. The simplified expression is 6x^2 + x.

9. Simplify the expression (2x^3 - 4x^2 + 3x) / (x^2 - 1).

10. Evaluate the expression inside the parentheses: 2x^3 - 4x^2 + 3x.

11. Evaluate the expression in the denominator: x^2 - 1.

12. Divide the numerator by the denominator: (2x^3 - 4x^2 + 3x) / (x^2 - 1).

By following these steps, you can simplify a wide range of algebraic expressions. Remember to always check your work and ensure that the final expression is in its simplest form.