what is it mean to "foil" in math
suppose you have
(a+b)(c+d)
= ac + ad + bc + bd
ac is the product of the "firsts" --- f
ad is the product of the "outers" --o
bc is the product of the "inners" ---i
bd is the product of the "lasts" ----l
hence "foil"
In mathematics, "FOIL" is an acronym that stands for First, Outer, Inner, Last. It is a method used to multiply two binomials, which are expressions that consist of two terms connected by addition or subtraction. The FOIL method helps to remember the order in which you multiply the terms within the binomials.
To "foil" two binomials, follow these steps:
1. First, multiply the First terms of each binomial.
2. Then, multiply the Outer terms of each binomial.
3. Next, multiply the Inner terms of each binomial.
4. Finally, multiply the Last terms of each binomial.
After multiplying each pair of terms, combine the like terms and simplify the resulting expression, if necessary.
Here's an example to illustrate the FOIL method:
Let's say we want to multiply the binomials (2x + 3) and (4x - 5).
Using the FOIL method:
1. Multiply the First terms: (2x) * (4x) = 8x^2
2. Multiply the Outer terms: (2x) * (-5) = -10x
3. Multiply the Inner terms: (3) * (4x) = 12x
4. Multiply the Last terms: (3) * (-5) = -15
Now, combine the like terms: 8x^2 - 10x + 12x - 15
Simplifying further: 8x^2 + 2x - 15
So, "foiling" refers to the process of multiplying two binomials using the FOIL method.