Algebraic Expressions: Free Course

About this course

An algebraic expression represents a quantity or relationship without necessarily asserting an equation. This course develops variables, evaluation, equivalent forms, expansion and factoring. Study the complete public source playlist from Khan Academy in English, with all 15 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Write and interpret expressions with variables.
• Evaluate expressions by substitution.
• Combine like terms and apply the distributive property.
• Recognize equivalent expanded and factored forms.

Skills you’ll gain

• Variables
• Expression evaluation
• Like terms
• Distributive property

Course Overview

The introductory recordings explain the role of a variable and the notation used for multiplication. Substitution examples include one or two variables and contextual quantities. Combining like terms requires attention to the variable part of each term, while the distributive property supports both expanding a product and factoring a common factor. Fraction examples extend the same structural reasoning to less familiar forms. The source also contrasts equivalent ways of writing an expression. Keep the original expression's meaning in view: a shorter-looking form is useful only if it remains equivalent for the values under consideration.

How to study the course

• Videos 1–3: this part of the source list includes “How to simplify a big expression by combining like terms” through “Example: Evaluating expressions with 2 variables”. State the quantities and conditions before calculating. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 4–7: this part of the source list includes “Combining like terms introduction” through “Expressions with two variables”. Keep equivalent expressions or representations connected. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 8–11: this part of the source list includes “How to combine like terms” through “How to expand an expressions using the distributive property”. Check each operation with a small example before extending it. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 12–15: this part of the source list includes “Algebraic expressions with fraction division” through “Algebraic expression adding fractions”. Explain a result in words as well as symbols. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, returning learners and anyone strengthening the specific mathematics named in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort with the preceding arithmetic or algebra skills is useful. Keep paper, a pencil and a calculator when a lesson uses one. Grade-specific courses assume the learner’s earlier grade-level knowledge.

Put the lessons into practice

Write an expression for a fictional cost with a fixed charge and a per-item charge. Evaluate it for two quantities. Create a separate expression with brackets and like terms, simplify it and check both forms at several values. Explain why terms with different variable parts cannot simply be combined.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.