Multiplying Polynomials
Distribute every term of one factor across the other.
Key idea
Distribute every term of one factor across the other.
In depth
Multiply each term of one polynomial by each term of the other, then combine like terms. This is repeated use of the distributive property; an area model keeps track.
Worked example
(x + 2)(x² − x + 3) = x³ − x² + 3x + 2x² − 2x + 6 = x³ + x² + x + 6.
Real-world uses
- Expanding the area of a rectangle with variable sides
- Building formulas for packaging volumes
Common mistake
Missing a cross term. With m and n terms there are m × n products.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Multiplying Polynomials?
Distribute every term of one factor across the other. It is a topic at the intermediate level in Algebra.
Where is Multiplying Polynomials used in real life?
Real-world examples: Expanding the area of a rectangle with variable sides; Building formulas for packaging volumes.
What should I learn before Multiplying Polynomials?
Make sure you are comfortable with Adding and Subtracting Polynomials, the previous topic in Algebra.
What is a common mistake with Multiplying Polynomials?
Missing a cross term. With m and n terms there are m × n products.
How can I practise Multiplying Polynomials?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Multiplying Polynomials?
Move on to FOIL Method next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.