• MathsFirst Home
• Online Maths Help
  • Notation
  • Arithmetic
    • Decimals
    • Fractions
    • HCF and LCM
    • Order of Operations
    • Signed Numbers
  • Algebra
    • Exponents
      • Integer Exponents
      • Fractional Exponents
      • Exponents Worksheet
    • Combining Like Terms
    • Simple Expansions
    • Factorisation
    • Mathematical Formulae
      • Constructing Formulae
      • Rearranging Formulae
        • Order of Operations for Algebraic Expressions
        • Inverse Operations and Functions
        • Rearranging Equations I (Simple Equations)
        • Rearranging Equations II (Quadratic Equations)
        • Rearranging Equations III (Harder Examples)
      • Area, Surface Area and Volume Formulae
    • Coordinate Systems and Graphs
    • Linear Equations & Graphs
    • Simultaneous Linear Equations
    • Polynomials
    • Quadratic Polynomials
    • Rational Functions
    • Logarithms
  • Calculus
    • Differentiation
      • Tangents, Derivatives and Differentiation
      • The Basic Rules
      • Products and Quotients
      • Chain Rule
      • Logarithmic Differentiation
      • Mixed Differentiation Problems
      • Sign of the Derivative
      • Sign of the Second Derivative
    • Integration
      • Basic Integrals
      • Multiple, Sum and Difference Rules
      • Linear Substitution
      • Simpler Integration by Substitution
      • Harder Integration by Substitution
      • Trig Substitution 1
      • Trig Substitution 2
      • Integration by Parts
  • Trigonometry
    • Pythagoras Theorem
    • Trig Functions and Related Topics
• First Year Maths Pathways
• Readiness Quizzes
• Study Maths
  at Massey
  • Undergraduate
  • Postgraduate
• Other Math Links
• About MathsFirst
• Contact Us

Like Terms

Description

A term is a number, variable or the product of a number and variable(s).

Here are some terms:

-2, 4x, -xy, 7x², 100xy³, , abc, ax², 0.5x

A constant term is a number.

A coefficient is the numeric factor of a term. A constant term is a special case of a coefficient. The coefficients of the terms below are highlighted in red:

-2, 7x², 100xy³, 0.5x

The coefficient of    x = 1x   is 1 and the coefficient of   -x = -1x   is -1. The coefficient of is .

Two terms are called like terms if they differ by a constant factor. That is, only their numerical coefficients are different.
Constant terms are like terms.

Exercise 1.

The following are like terms:

2x, 1000x, -5x, 0.65x, (2/3)x

And these are like terms:

7x², 21769x², 0.778x², -41x², (6/7)x²

But none of the following are like terms:

2x, 2x⁵, 2x^-2, 2x^0.5, 2x^(4/3)

as the power of x differs in the different terms.

Exercise 1.

Got it? Good! Now try some of the following exercises. Each time you click on "Next Exercise" a new exercise will appear.

| Like Terms Index | Combining Like Terms 1 >>