Subtracting Polynomials

Learn to subtract polynomial expressions correctly. Grade 9 Alberta mathematics.

Lesson 5.4 of Polynomials in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Understanding Subtraction of Polynomials. Learn what it means to subtract one polynomial from another and how signs affect each term.
• Subtracting Polynomials Using Algebra Tiles. Use algebra tiles to visualize subtraction and understand how positive and negative tiles represent terms.
• Subtracting Polynomials Algebraically. Simplify polynomial subtraction by changing signs and combining like terms.
• Applying Subtraction of Polynomials. Apply polynomial subtraction to real-world problems and practice identifying common mistakes.

Inside the lesson — a free preview

What Does It Mean to Subtract?

To subtract polynomials, we just need to add the opposite.Remember, opposite numbers have a sum of zero.

Opposite Polynomials

The same idea works with polynomials — opposite polynomials also have a sum of zero.

For example:

Finding the Opposite of Binomials and Trinomials

How do we get the opposite of a binomial or trinomial? Flip the sign of every term.

Key Idea

When Subtracting Polynomials. A − B = A + (−B)

To subtract, change the signs of all the terms in the second polynomial, then add.

The Subtraction Rule

We can subtract polynomials just like we did with addition — but instead of combining directly, we add the opposite of the second polynomial.

To subtract polynomials, follow these steps:

Overview

Let's apply what we've learned about subtracting polynomials to real-world and multi-step problems.

Worked example: Horizontal Method

Subtract the following: (3x² + 5x − 4) − (x² − 2x + 7)

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