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

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