Combine like terms and simplify polynomial expressions. Grade 9 Alberta math lesson.
Lesson 5.2 of Polynomials in Grade 9 Math — Alberta curriculum lessons.
A term is a single part of a polynomial expression.
Each term can be:
✅ Example:In the expression 4x² + 3x − 7 there are three terms: 4x²; 3x; −7 Terms are always separated by + or − signs.
Each term has three main parts:. Example: 5x² = 5 * x * x
A coefficient is the number that multiplies a variable in a term. It tells us how many times we’re using that variable.
Examples:
Like terms have the same variable(s) raised to the same exponent(s).
Only the coefficients can be different.
✅ Examples of like terms:
They can be combined because their variable parts match.
Unlike terms have different variables or different exponents, so they cannot be combined.
❌ Examples of unlike terms:
Each remains separate in a polynomial.
When simplifying a polynomial, terms with the same variables and exponents can be combined into one term.
Only the number part (coefficient) changes — the variable stays the same.
✅ Example:2x + 5x Both terms have the same variable, x.; We add the coefficients → 2 + 5 = 7.; The variable x stays the same.
✅ Simplified Expression:
7x
Algebra tiles are visual tools that show each term using coloured blocks. They help you see how like terms combine and cancel out.
Mike was asked to write an expression equivalent to 2x − 7 − 4x + 8. Below are his workings.
His solution:
What error did he make? Show the correct simplification.
Answer:
✅ The correct answer is −2x + 1, not 2x − 1.
Example 1 – Adding Like TermsSimplify: 2x + 3x Step 1: Both terms have the same variable x.; Step 2: Add the coefficients (2 + 3 = 5).; Step 3: Keep the variable x. ✅ Answer: 5x
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.