Simplifying Algebraic Expressions: Combining Like Terms

Algebraic Expressions: Simplifying and Combining Like Terms

Algebraic expressions are mathematical combinations of variables, numbers, and operations like addition, subtraction, multiplication, and division. In this article, we'll focus on simplifying expressions and combining like terms, which are essential skills in algebra.

Simplifying Expressions

Simplifying mathematical expressions means evaluating and rewriting them in a more compact form without changing their equivalent value. To simplify expressions, follow these steps:

1. Combine like terms by adding or subtracting similar expressions.
2. Perform operations within parentheses.
3. Simplify fractions by finding common denominators for like terms.

For example, let's consider the expression: 3x - 2 + 5x + 7. First, combine like terms:

3x + 5x = 8x

Then, add the constants:

8x + 2 + 7 = 8x + 9

So, the simplified expression is 8x + 9.

Combining Like Terms

Combining like terms involves adding or subtracting expressions that have the same variable and exponent. For example, in the expression 4x + 6x - 2x + 17, the like terms are all the terms with the variable x. To combine these like terms, add or subtract them:

4x + 6x - 2x = 8x

The simplified expression is 8x + 17.

Cautions

• Do not simplify expressions with different variables or exponents together. For example, do not combine 2x + 3y with 4x - 7z, as these terms have different variables and cannot be combined.
• Do not combine terms inside and outside parentheses together. For example, do not combine 5x + 3(2x - 7) with just 5x, as the terms inside the parentheses need to be simplified first.

Practice Problem

Simplify the expression: 2(x + 5) - 3x + 7.

First, distribute the 2 to the term inside the parentheses:

2(x + 5) = 2x + 10

Now, combine like terms:

2x + 10 - 3x = -x + 10

Add the constant:

-x + 10 + 7 = 3

The simplified expression is 3.

In conclusion, simplifying algebraic expressions involves combining like terms and performing operations on terms with the same variables and exponents. This skill is essential in solving algebraic equations and expressions effectively. Practice is key to becoming proficient in simplifying algebraic expressions, and using a systematic approach can make the process easier and more organized.