Concept Overview
An algebraic expression is a mathematical phrase made with numbers, variables, and operations.
Before solving equations, students must know how expressions are built.
Terms, Coefficients & Like Terms explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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An algebraic expression is a mathematical phrase made with numbers, variables, and operations.
Before solving equations, students must know how expressions are built.
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This lesson explains terms, coefficients, constants, like terms, and simple simplification.
An expression does not have an equals sign. For example, 3 is an expression.
A term is one part of an expression separated by plus or minus signs. In 3, the terms are 3x and 5.
A coefficient is the number multiplying a variable. In 3x, the coefficient is 3.
Like terms have the same variable part. You can add or subtract only like terms.
Meaning: Variables can change. Constants stay fixed.
Definition: A variable is a letter used for a number. A constant is a number without a variable.
In 4, x is the variable and 7 is the constant.
Meaning: Terms are the separate parts of an expression.
Definition: A term is separated by plus or minus signs.
In 5, the terms are 5a, -3b, and 9.
Meaning: A coefficient tells how many of a variable term there are.
Definition: The coefficient is the numerical factor of a variable term.
Ix, the coefficient i. In y, the coefficient is 1.
Meaning: Like terms have the same variable part.
Definition: Like terms have the same variables raised to the same powers.
3x and 7x are like terms. 3x and 3y are unlike terms.
Easy
Question: Identify the coefficient op.
Medium
Question: Simplify 4.
Exam-level
Question: Simplify 3.
Combining unlike terms
Why it happens: Students add any terms that appear close together.
Correct approach: Combine only terms with the exact same variable part.
Dropping the sign before a term
Why it happens: The minus sign is treated as an operation only.
Correct approach: Carry the sign with the term when rearranging.
Thinking x has coefficient 0
Why it happens: No number is written before x.
Correct approach: The coefficient of x is 1.
Is 3 an equation?
No. It is an expression because it has no equals sign.
Are 2x and 2y like terms?
No. The variables are different.
Can constants be like terms?
Yes. All constants are like terms with other constants.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.