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how to use the foil method

Remember, FOIL is an acronym that tells you how to multiply one parenthetical expression by another. It stands for "First, Outside, Inside, Last," which is the order in which you multiply and then add the elements in your expression. The confusing part is that "First" and "Last" refer to an element's position within it's parenthetical expression, while "Outside" and "Inside" refer to an element's position within the whole expression. This means each element is called two things: 1) Either "First" or "Last" and 2) Either "Outside" or "Inside."

Using the example from above, I've labeled each element with two labels: F for First, O for Outside, I for Inside and L for Last. I've made one x orange and the other green, to help you keep track of which one I'm talking about, but the orange x and the green x are still the same variable.

FO    LI      FI     LO

( x +  2)  *  (x  +  3)

Step 1: Multiply the First element from each parenthetical expression by the other --> x * x = x2

Step 2: Multiply the Outside elements of the overall expression by each other --> x * 3 = 3x

Step 3: Multiply the Inside elements of the overall expression by each other --> 2 * = 2x

Step 4: Multiply the Last element of each parenthetical expression by the other : 2 * 3 = 6

Step 5: Add them all together --> x2 + 3x + 2x + 6

Step 6: Simplify --> x2 + 5x + 6

I will try and make this as simple on here as I can

Let's take the example

(x+2)(x+3) I will call the x in the first parentheses X1 and the other X2

First, you would take X1 and multiply it by X2 which equals x2. (Basically, we took the first number of the first equation times the first number of the second equation)

Next, we will multiply X1 by 3 which equals 3x. (So this time we took the first number of the first equation and multiplied it be the second number in the second equation.

Now the first X1 is all done and we have to use the second number in the first equation which is 2 and do the same thing

2 times x = 2x

2 times 3 = 6

For the next step you have to look at the equation and what signs they have. We have both pluses so we can just add our numbers together.

x2  + 3x + 2 x + 6= x2 + 5x + 6.

I hope this helps, if not, give me an example from your homework or whatever you are stuck on and I will try another example.

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