Adding Polynomials

Master adding polynomial expressions with multiple terms. Grade 9 Alberta mathematics curriculum.

Lesson 5.3 of Polynomials in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Adding Polynomials with Algebra Tiles. Use tiles to visualize how polynomial terms combine when added together.
• Adding Polynomials Algebraically. Learn how to add polynomials by combining like terms step-by-step.
• Applying Addition of Polynomials. See how to align polynomials vertically to add like terms easily.

Inside the lesson — a free preview

What Does It Mean to Add Polynomials?

When we add polynomials, we combine like terms. Algebra tiles help us visualize this process by showing each term as a physical object.Blue tiles represent positive x² and x values, green tiles represent positive constants, and red tiles represent negative values.

What Does It Mean to Add Polynomials?

To add polynomials, we combine like terms by adding the coefficients (number parts) of each matching variable term.Polynomials can be added in two ways — horizontally or vertically. Both give the same result — the vertical method just makes it easier to see like terms.

Method 1: Horizontal Addition

When adding horizontally, we remove the brackets and combine like terms together.

Method 2: Vertical Addition

When adding vertically, we stack the polynomials and line up like terms in columns. This makes it easier to see which terms to combine.

Introduction

Now that we've learned how to add polynomials both with tiles and algebraically, let's apply that knowledge to solve real-world problems and check for mistakes in solutions.

Worked example: – Horizontal Method

Simplify: (4x² + 2x + 1) + (2x² + 5x + 6)Step 1: Write without brackets.4x² + 2x + 1 + 2x² + 5x + 6Step 2: Combine like terms.(4x² + 2x²) + (2x + 5x) + (1 + 6)✅ Final Answer: 6x² + 7x + 7

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