Question

simplify | (7-sqrt(2)) (8+sqrt(2))

Answer 1

\[(7-\sqrt{2})(8+\sqrt{2})\]
This question should be answered using FOIL.
First -> Outside -> Inside -> Last

Answer 2

How do I do that?

Answer 3

7 and 8 are the First terms.
\[-\sqrt2 and + \sqrt2 \]
are the Last terms.
Inside are the two terms in the middle
Outside are the two terms on either end.
Does that make sense?

Answer 4

Multiply the first terms together, then the Inside terms, then the outside terms, then the last terms. Add them all together (using appropriate signs) and combine like terms.

Answer 5

so would it end being 56sqrt2 ?

Answer 6

No. Can you show me your work, one step at a time?

Answer 7

First
\[7 * 8 = 56\]
Inside:
\[8 * -\sqrt2 = -8\sqrt2\]
Outside:
\[7 * \sqrt2 = 7\sqrt2\]
Last:
\[-\sqrt2 * \sqrt2 = -\sqrt4 = -2\]

Answer 8

Do you understand where each of these equations come from?

Answer 9

Kind of

Answer 10

First:
The product of the first terms in each group.

Answer 11

Outside:
The product of the terms farthest from the center.

Answer 12

Inside:
The product of the terms closest to the center.

Answer 13

Last:
The product of the last terms in each group.

Answer 14

Make more sense now?

Answer 15

Yes actually

Answer 16

Great! So, know you add all of the terms together. Don't try to combine like terms just yet. Write out your equation. Use the Equation button under the reply box to write a properly formatted equation. (It's easier to read)