Question

How do you simplify `(sqrt12 - sqrt2)(sqrt12 + sqrt2)`?

Answer 1

`(sqrt12-sqrt2)(sqrt12+sqrt2)=10`

Explanation:

To simplify `(sqrt12-sqrt2)(sqrt12+sqrt2)`, we use the difference of two squares

`(a+b)(a-b)=a^2-b^2`

So

`(sqrt12-sqrt2)(sqrt12+sqrt2)=(sqrt12)^2-(sqrt2)^2=12-2=10`

Answer 2

`10`

Explanation:

`(sqrt12 - sqrt2)(sqrt12 + sqrt2)`

There are two ways to solve this, and I'm going to show the longer way first.

METHOD 1:

To solve this, we distribute and expand using the FOIL method:

First, multiply the "firsts":
`sqrt12 * sqrt12 = sqrt144 = 12`

Then the "outers":
`sqrt12 * sqrt2 = sqrt24`

Then the "inners":
`-sqrt2 * sqrt12 = -sqrt24`

Finally the "lasts":
`-sqrt2 * sqrt2 = -sqrt4 = -2`

When we combine these expressions we get:
`12 + sqrt24 - sqrt24 - 2`

The `sqrt24` and `-sqrt24` cancel each other out, so we're left with:
`12 - 2`

Which simplifies down to:
`10`

METHOD 2:

To solve this, we use:

This expression `(sqrt12 - sqrt2)(sqrt12 + sqrt2)` is in the form `(a-b)(a+b)`, which is the same as `(a+b)(a-b)`.

As we can see, this is equivalent to `a^2 - b^2`, so it becomes:
`sqrt12^2 - sqrt2^2`

Simplify:
`12 - 2`

So the final answer is:
`10`

Hope this helps!