Discover insights, ideas, and tips from our latest articles.
By eMATHinstruction
Algebra is really about representing relationships between quantities. It uses variables to stand for numbers that can vary, and when you combine numbers and variables using multiplication or division, you create terms. When those terms are then connected through addition or subtraction, you get an expression.
A simple expression might look like:
5x^2 – 2x + 10
This expression has three terms, and each term depends on the value of x. Think of terms as separate pieces that come together only at the end. Keeping the structure clear is important, especially as expressions get more complicated.
You can follow along with this topic in our teacher guided lesson video.
Algebra is really about representing relationships between quantities. It uses variables to stand for numbers that can vary, and when you combine numbers and variables using multiplication or division, you create terms. When those terms are then connected through addition or subtraction, you get an expression.
A simple expression might look like:
5x^2 – 2x + 10
This expression has three terms, and each term depends on the value of x. Think of terms as separate pieces that come together only at the end. Keeping the structure clear is important, especially as expressions get more complicated.
One of the most important skills in Algebra 2 is evaluating expressions. If x = -2, then evaluating 5x^2 – 2x + 10 simply means replacing x everywhere it appears.
5(-2)^2 – 2(-2) + 10
20 + 4 + 10 = 34
Every term gets evaluated on its own. Only after that do you add everything together. This process might feel basic, but it is the same process you’ll use when evaluating polynomial functions, rational functions, and even expressions inside formulas in chemistry or physics.
Zeros play a huge role in this course. A zero is simply a value of x that makes an expression equal to zero.
Take the expression:
x^2 – 2x – 8
If x = 4, then
16 – 8 – 8 = 0
That means x = 4 is a zero. Zeros tell you important things about the behavior of expressions and, later on, the behavior of graphs. Little by little, you’ll see how these become the x-intercepts of quadratic and polynomial functions.
Another example is:
x^2 – 64
To find its zeros, ask yourself: for what values of x will x^2 equal 64?
The answers are 8 and -8. So the expression has two zeros, which is common with quadratics.
Rational expressions are expressions written as fractions, like:
(x – 10) / (x + 2)
Just like before, evaluate the expression by substituting values for x. If x = 0, you get −10 divided by 2, which is −5. If x = 10, the numerator becomes zero, which makes the entire expression equal to zero.
A fraction is only zero when its numerator is zero. This single fact will help you quickly find the zeros of any rational expression.
It is also important to notice when an expression becomes undefined. If x = -2, the denominator of this expression becomes zero. Division by zero is not allowed, so x = -2 is an excluded value. Later in the course, you will see how these excluded values show up as vertical asymptotes on graphs.
Here is another example:
(x^2 – 25) / (x^2 – 81)
This expression equals zero when the numerator equals zero, which happens at x = 5 or x = -5. It is undefined when the denominator equals zero, which happens at x = 9 or x = -9. Understanding how to identify these values will be important later when you simplify, solve, and graph rational functions.
Sometimes expressions involve more than one variable. For example:
5x^2 – 12y^3
Evaluating an expression like this means substituting each variable carefully and following the order of operations. If x = 3 and y = -2, you square x, cube y, and work through each part step by step.
These kinds of expressions are common in science and engineering, where multiple quantities change at the same time. Becoming comfortable with substitution now will help you interpret formulas in many different contexts.
Expressions are everywhere in Algebra 2. They form the backbone of equations, functions, graphs, and many of the techniques you will learn this year. Understanding how expressions are built, how to evaluate them, and what their zeros and undefined values represent will help make the more advanced topics feel much more approachable.
Keep practicing, and remember that every new skill becomes clearer the more you work with it. Algebra builds from these foundations, and you are already learning the structure you will need for everything that comes next.
We’re here to make teaching easier. Get your free teacher trial here.
Lesson planning, grading, and organizing materials can take up hours of precious time. Having ready-to-use resources means less stress and more space to focus on students. With the right tools, teachers can spend their energy on what matters most: inspiring a love of math and helping every learner succeed.
Thank you for using eMATHinstruction materials. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. Using these materials implies you agree to our terms and conditions and single user license agreement.
Thank you for using eMATHinstruction materials. In order to continue to provide high quality mathematics resources to you and your students we respectfully request that you do not post this or any of our files on any website. Doing so is a violation of copyright. Using these materials implies you agree to our terms and conditions and single user license agreement.
The content you are trying to access requires a membership. If you already have a plan, please login. If you need to purchase a membership we offer yearly memberships for tutors and teachers and special bulk discounts for schools.
Sorry, the content you are trying to access requires verification that you are a mathematics teacher. Please click the link below to submit your verification request.
To start your free trial, please log in to your account.