can you please explain to me what the letters suppose to mean on this algebra problems that are in the foil method

## i still dont understand what the x means or what each letter supoose to mean

# 1 Answer

Letters are the labels or names for variables, and a variable is something that can change, like the speed limit on roads and highways. Here is an example:

In many states, if you drive 15 mph over the speed limit you are ticketed for reckless driving. So if x represents the speed limit, and the police clock you driving at x + 15 they can give you a ticket for reckless driving. If the speed limit = 55, then x + 15 = 70. If the speed limit is 30, then x+ 15 = 45. We use an equation with variable x to mathematically express the reckless driving law, x + 15 = reckless driving. No matter what the speed limit might be, you can put it in for x and find the speed for a reckless driving ticket.

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FOIL is a "recipe" to multiply 2 expressions with variables to get their product.

If we are trying to multiply (x + 7) by (2x - 4) we notice the each of the expressions has 2 terms.

In (x + 7), the x is the First term and the 7 is the Last term.

In (2x - 4), the 2x is the First term and the -4 is the Last term.

Write the letters for FOIL vertically and look at your problem (x + 7)(2x - 4)

**F**: Mulitply the **first** terms x times 2x = 2x^{2} (remember x^{2} just means x times x)

**O**: Multiply the **outside** terms x times -4 = -4x

**I**: Multiply the **inside** terms 7 times 2x = 14x

**L**: Multiply the **last** terms 7 times -4 = -28

Then add every answer together and combine the like terms: 2x^{2 }+ (-4x) + 14x + (-28)

The only terms that can add together are -4x and 14x. They both have x (notice x^{2} is different) so add -4 and 14 to get 10, so -4x + 14x = 10x

Nothing else combines, so just write it down: 2x^{2} + 10x + (-28)

When you add a negative, that is the same as subtracting, so this becomes 2x^{2} + 10x - 28