Expanding Binomials
Expanding binomials means multiplying two bracket expressions together. The FOIL method (First, Outer, Inner, Last) helps organise the four multiplications needed.
What You Need to Know
Key Concept Diagram
FOIL stands for First, Outer, Inner, Last - the four pairs you multiply
(a + b)(c + d) = ac + ad + bc + bd
Collect like terms after expanding to simplify the result
Perfect squares: (a + b)^2 = a^2 + 2ab + b^2
Key Vocabulary
Binomial
An algebraic expression with exactly two terms
FOIL
A method for expanding two binomials: First, Outer, Inner, Last
Like terms
Terms with identical variable parts that can be combined
Perfect square
The result of squaring a binomial: (a+b)^2 = a^2 + 2ab + b^2
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Expand (x + 3)(x + 5):
Question 2
Expand (x - 2)(x + 4):
Question 3
Expand (x + 3)^2:
Key Concepts Summary
- ●FOIL stands for First, Outer, Inner, Last - the four pairs you multiply
- ●(a + b)(c + d) = ac + ad + bc + bd
- ●Collect like terms after expanding to simplify the result
- ●Perfect squares: (a + b)^2 = a^2 + 2ab + b^2