Algebraic Expressions Study Guide: GED Math (page 2)

Evaluating Algebraic Expressions

Algebraic expressions have specific values only when the variables have values. Finding the value of an algebraic expression by plugging in the known values of its variables is called evaluating an expression.

Examples

1. Evaluate 5 ÷ (x + y), when x = 2 and y = 3.

Plug the numbers into the algebraic expression: 5 ÷ (2 + 3).

Solve by following the order of operations. Add the numbers in parenthesis: 5 + (2 + 3) = 5 + 5.

Divide to find the final answer: 5 ÷ 5 = 1.

2. Find the value of 5 + x, when x = –2. Plug the numbers into the algebraic expression:

5 + (–2).

Solve: 5 – 2 = 3.

Simplifying Algebraic Expressions

The parts of an algebraic expression are called terms. A term is a number, or a number and the variables associated with it. For example, the following algebraic expression has three terms:

algebraic expression: 5x² – 5x + 1

terms: +5x², –5x, +1

As you can see, the terms in an algebraic expression are separated by + and – signs. Notice that the sign in front of each term is included as part of that term—the sign is always part of the term. If no sign is given, it is positive (+).

Simplifying an algebraic expression means to combine like terms. Like terms are terms that use the same variable and are raised to the same power. Here are some examples of like terms.

When you combine like terms, you group all the terms that are alike together. This makes it easier to evaluate the expression later on.

Examples

1. Simplify the following algebraic expression: 5x + 3y + 9x.

Write the like terms next to each other. You know that 5x and 9x are like terms because they both have x. So write them next to each other: 5x + 9x +3y.

Combine the like terms. In this case, add them: 5x + 9x + 3y = 14x + 3y.

You can't simplify the 3y because there are no other terms in the expression with the variable y. So you leave it alone. The simplified expression is 14x + 3y.

2. Simplify the following algebraic expression: 2x² + 3y + 9xy + 3y².

You cannot write the like terms next to each other, because there are no like terms in this expression. It is already simplified.

3. Simplify the following algebraic expression: 5x(2x – 1) + 9x.

Write the like terms next to each other. Begin by distributing the 5x so that you can remove the parentheses. Multiply 5x(2x – 1): 10x² – 5x.

So now the expression is 10x² – 5x + 9x.

Now you can see that –5x and 9x are like terms because each contains the x term.

Combine the like terms. Add the like terms: –5x + 9x = 4x.

Now your expression is simplified to 10x² – 4x.

You can't simplify further because there are no other terms in the expression with the same variable. Therefore, the simplified expression is 10x² – 4x.

When combining like terms, begin by solving to remove the parentheses. If a negative sign is in front of a set of parentheses, it affects every term inside the parentheses. Here's an example.

Example

–2(x – 3y + 2)

When you multiply each term inside the parentheses by –2, the result is –2x + 6y – 4.

Notice that the negative sign (–) affects each term inside the parentheses.

Practice problems for these concepts can be found at:

Algebra and Functions Practice Problems: GED Math