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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