FOIL Method
Multiply two binomials: First, Outer, Inner, Last.
Key idea
Multiply two binomials: First, Outer, Inner, Last.
In depth
FOIL (First, Outer, Inner, Last) is a memory aid for multiplying two binomials: (a + b)(c + d) = ac + ad + bc + bd. It is just the distributive property done carefully.
Worked example
(x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15.
Formula
Real-world uses
- Expanding (x + 3)(x − 2) to find a rectangle area or solve for roots of a quadratic
Common mistake
Writing x² + 15 and forgetting the middle terms.
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 FOIL Method?
Multiply two binomials: First, Outer, Inner, Last. It is a topic at the intermediate level in Algebra.
What is the formula for FOIL Method?
The key formula is (a+b)(c+d) = ac+ad+bc+bd.
Where is FOIL Method used in real life?
Real-world examples: Expanding (x + 3)(x − 2) to find a rectangle area or solve for roots of a quadratic.
What should I learn before FOIL Method?
Make sure you are comfortable with Multiplying Polynomials, the previous topic in Algebra.
What is a common mistake with FOIL Method?
Writing x² + 15 and forgetting the middle terms.
How can I practise FOIL Method?
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 FOIL Method?
Move on to Special Products 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”.