Multiplying Binomials Using FOIL
Multiplying binomials using FOIL is a core Grade 9 Algebra 1 skill in California Reveal Math (Unit 9: Polynomials). FOIL stands for First, Outer, Inner, Last — the four term pairs you multiply when expanding (a+b)(c+d). For (x+3)(x+5): First=x^2, Outer=5x, Inner=3x, Last=15, combining to x^2 + 8x + 15. For (3x-2)(3x+2), the inner and outer terms cancel, giving 9x^2 - 4. FOIL applies specifically to binomial-times-binomial multiplication.
Key Concepts
The FOIL method is a shortcut for multiplying two binomials. FOIL stands for First, Outer, Inner, Last — the four pairs of terms you multiply:.
$$(a + b)(c + d) = \underbrace{ac} {\text{First}} + \underbrace{ad} {\text{Outer}} + \underbrace{bc} {\text{Inner}} + \underbrace{bd} {\text{Last}}$$.
Common Questions
What does FOIL stand for in algebra?
FOIL stands for First, Outer, Inner, Last. These are the four pairs of terms you multiply when expanding two binomials: (a+b)(c+d) = ac + ad + bc + bd.
How do you use FOIL to multiply (x+3)(x+5)?
First: x*x = x^2. Outer: x*5 = 5x. Inner: 3*x = 3x. Last: 3*5 = 15. Combine like terms: x^2 + 8x + 15.
How do you use FOIL to multiply (2x-4)(x+7)?
First: 2x^2. Outer: 14x. Inner: -4x. Last: -28. Combine: 2x^2 + 10x - 28.
What happens with (3x-2)(3x+2)?
First: 9x^2. Outer: 6x. Inner: -6x. Last: -4. The outer and inner terms cancel: result is 9x^2 - 4. This is a difference of squares pattern.
Does FOIL work for multiplying more than two binomials or longer polynomials?
No. FOIL is specifically a memory device for binomial times binomial. For larger polynomials, use the horizontal or vertical distribution method to ensure every term is multiplied.