Multiplying Polynomials
Multiply each term by each term, then combine like terms.
About this topic
To multiply polynomials, use the distributive property so that every term in the first multiplies every term in the second, then collect like terms. For binomials this is the FOIL method (First, Outer, Inner, Last), and an area model gives a helpful picture.
Multiplying two binomials gives up to four terms before combining. For (x + 3)(x + 5): first x², outer 5x, inner 3x, last 15, so the product is x² + 8x + 15. An area model draws a rectangle with sides x + 3 and x + 5 split into four smaller rectangles, whose areas are exactly those four terms. A trinomial times a binomial gives six products to combine.
This skill is used when computing areas and volumes of boxes with variable dimensions, and when expanding expressions in probability and finance. It is also the reverse process of factoring, so mastering it helps later.
Typical errors include multiplying only the first terms, forgetting the middle terms, and mishandling signs. Remember that the degree of a product is the sum of the degrees of the factors, so a quadratic times a quadratic gives a degree 4 polynomial, which is a good quick check.
Key ideas
- FOIL works for two binomials
- Use the area model to organise
- Degrees add
Quick check
Use cases: where Multiplying Polynomials helps
- Homework: review the key idea behind Multiplying Polynomials before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Multiplying Polynomials without notes.
- Visual learning: play with the interactive lab to see how Multiplying Polynomials changes when you adjust its inputs.
- Teaching a friend: explain Multiplying Polynomials in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Multiplying Polynomials?
Multiply each term by each term, then combine like terms.
What will I learn in Multiplying Polynomials?
FOIL works for two binomials. Use the area model to organise. Degrees add.
Is Multiplying Polynomials part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Multiplying Polynomials lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Multiplying Polynomials?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.