# What is Algebraic Expression | TakeLessons Blog

Who doesn’t like a good mystery? Challenges like “whodunnits” exercise our brains, make us think, and give us a feeling of reward when we get the right answer.

Math has its own whodunnit in the form of algebraic expression. In terms of algebraic expression mysteries, you’re not looking for an answer such as, “the butler did it,” but instead trying to find a number that’s not immediately apparent.

[Picture of butler’s hands holding napkin or tray]

Solving the mystery of “what is algebraic expression?” is an exercise that will open you up to more complicated math should you choose to become one of the following:

• Engineer
• Scientist
• Doctor
• Researcher
• Project planner
• Programmer
• Coder

These jobs use complex math every day. People in these professions don’t even necessarily need a calculator to solve some of these equations, either. That’s how familiar people can get with complicated algebra.

Because many high-level jobs require knowledge of algebraic expression, we’ll give you some algebraic expression examples with answers so you can learn to solve them yourself.

## What Is Algebraic Expression?

Algebraic expressions are, at their core, part of a math problem that has some unknown numbers hidden behind letters. It helps to know some definitions.

Variables: These are unknown numbers represented by letters, typically x, y, or z.

Constants: These are the numbers we can see and can be easily recognizable numbers such as 5, 22, -4, or even 0, but could also be more complicated such as fractions like ¼, or square roots such as √8.

Terms: A term could be a variable on its own, a constant on its own, or a combination of the two by multiplication or division.

For example, some terms of algebraic expression are 3x or (-8÷y). When a constant is right next to a variable, such as with 3x, that implies that they will be multiplied.

Coefficients: These are the numbers that multiply the variables. For 3x, the coefficient would be 3.

Like Terms: These are terms that have the same variable, such as 5x and 10x. If your expression was 5x+10x, you could simplify this as 15x.

Unlike Terms: These are terms that have different variables, such as 5x and 10y. Because they are different, you can not simplify them any further. If your expression was 2x+3x+6y+4y, that could be simplified as 5x+10y, but that’s as far as you can go.

Some algebraic expression definition math examples would be 3x+9y or -22÷8x. The expression is only one part of the overall algebraic equation. 