Algebraic Expressions Study Guide

Algebraic expressions are mathematical expressions that contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to represent a wide range of real-world and mathematical problems.

Parts of an Algebraic Expression

An algebraic expression is made up of several parts:

Variables: These are symbols, usually letters like x, y, or z, that represent unknown values.
Constants: These are fixed values, such as numbers, that do not change.
Coefficients: These are the numbers that are multiplied by variables in the expression.
Mathematical Operations: These include addition, subtraction, multiplication, and division.

Examples of Algebraic Expressions

Here are some examples of algebraic expressions:

3x + 7y
2a - 5b
4x^2 + 3xy - 2
5m + 2n - 8p + 10

Simplifying Algebraic Expressions

One of the key skills in algebra is simplifying algebraic expressions. This involves combining like terms and performing operations to reduce the expression to its simplest form.

Evaluating Algebraic Expressions

Another important skill is evaluating algebraic expressions. This involves substituting values for the variables and then simplifying the expression to find the result.

Practice Problems

Here are some practice problems to help you understand algebraic expressions:

Simplify the expression 4x + 2x - 7
Evaluate the expression 3y - 2 for y = 5
Simplify the expression 2a^2 - 5a + 3a^2 - 4a

Remember, practice is key to mastering algebraic expressions. The more you practice, the more comfortable and confident you will become with using algebraic expressions.

Good luck!

◂Math Worksheets and Study Guides Eighth Grade. Real numbers

The resources above cover the following skills:

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]

Expressions and Equations

Work with radicals and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. [8-EE2]