Example Card: Multiplying Binomials Using the FOIL Method
Multiply binomials using the FOIL method in Grade 9 algebra. Apply First, Outer, Inner, Last multiplication to expand (a+b)(c+d) and combine like terms into a trinomial.
Key Concepts
The FOIL method is a clever mnemonic for multiplying binomials. This example demonstrates this key idea.
Example Problem.
Find the product of $(3b+4)(2b+2)$.
Common Questions
What is the FOIL method for multiplying binomials?
FOIL stands for First, Outer, Inner, Last — the four pairs to multiply. For (a+b)(c+d): F=ac, O=ad, I=bc, L=bd. Add all four products and combine like terms.
How do you use FOIL to multiply (2x+3)(x-5)?
F: 2x·x = 2x². O: 2x·(-5) = -10x. I: 3·x = 3x. L: 3·(-5) = -15. Add: 2x² - 10x + 3x - 15 = 2x² - 7x - 15.
Does FOIL work for polynomials with more than two terms?
FOIL applies specifically to two binomials. For larger polynomials use the distributive property: multiply each term in the first polynomial by every term in the second.