The FOIL method is a shortcut for multiplying two binomials, such as (a + b)(c + d). It helps you make sure every term in the first binomial is multiplied by every term in the second binomial. FOIL stands for First, Outer, Inner, Last, which names the four products you must find.
This method matters because it is used often in algebra, factoring, graphing quadratics, and solving equations.
Key Facts
- FOIL means First, Outer, Inner, Last.
- (a + b)(c + d) = ac + ad + bc + bd
- First: a · c = ac
- Outer: a · d = ad, Inner: b · c = bc
- Last: b · d = bd
- Combine like terms after multiplying, such as 3x + 5x = 8x
Vocabulary
- Binomial
- A binomial is an algebraic expression with exactly two terms, such as x + 4 or 2a - 7.
- FOIL
- FOIL is a method for multiplying two binomials by finding the First, Outer, Inner, and Last products.
- Term
- A term is a number, variable, or product of numbers and variables separated from other terms by addition or subtraction.
- Like terms
- Like terms have the same variable parts raised to the same powers, such as 4x and -9x.
- Area model
- An area model represents multiplication by splitting a rectangle into parts whose areas match the products of the terms.
Common Mistakes to Avoid
- Forgetting the inner or outer product is wrong because each term in the first binomial must multiply each term in the second binomial.
- Dropping a negative sign is wrong because subtraction belongs to the term that follows it, such as -3 in x - 3.
- Combining unlike terms is wrong because terms such as x^2 and x do not have the same variable power.
- Writing (x + 5)^2 = x^2 + 25 is wrong because (x + 5)^2 means (x + 5)(x + 5), so the middle terms must also be included.
Practice Questions
- 1 Use FOIL to expand (x + 3)(x + 7), then combine like terms.
- 2 Use FOIL to expand (2x - 5)(x + 4), then combine like terms.
- 3 Explain how the area model for (a + b)(c + d) shows the same four products as the FOIL method.