Question

How do you simplify `(-8-sqrt7)(-4+sqrt7)`?

Answer 1

Use the FOIL method in order to simplify the two binomials.

Explanation:

The FOIL method can be used when multiplying two binomials together. FOIL stands for First, Outsides, Insides, and Last. Let's go through each one together.

Firsts talk about the first term in each binomial. In this case, it's `-8` and `-4`. Let's multiply both of those together: `-8*-4=32`.

Next is Outsides, which are the first term in the first binomial and the second term in the second binomial (-8 and `sqrt(7)`, respectively). We could multiply those together and get -21.166..., but for the sake of keeping the answer as simple as possible, let's just keep the answer at `-8sqrt7`.

Next is Insides, the "inside" terms. Those terms are the two terms we didn't multiply in the Outsides, which are `-sqrt7` and `-4`. Again, for the sake of keeping the answer simple, let's just keep the answer at `4sqrt7`.

Lastly, we have, well, Last. They are the second terms in the binomials (`-sqrt7` and `sqrt7`). Multiplying a radical by itself gets rid of the radical because the number we get when multiplying is a square. For the Lasts, we have `-7`.

Now to wrap it all up. We now take all of the answers we got and add them: `32-8sqrt7+4sqrt7-7`. There's a catch with this problem, though: We can't add whole numbers and radicals together. So, we combine like terms (`32-7` and `-8sqrt7+4sqrt7`). This gets us our final answer of `25-4sqrt7`.