How do you simplify (√12−√2)(√12+√2)?

2 Answers
Monzur R.
Apr 28, 2018

(√12−√2)(√12+√2)=10

Explanation:

To simplify (√12−√2)(√12+√2), we use the difference of two squares

(a+b)(a−b)=a2−b2

So

(√12−√2)(√12+√2)=(√12)2−(√2)2=12−2=10

Shantelle
Apr 28, 2018

10

Explanation:

(√12−√2)(√12+√2)

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:
enter image source here
First, multiply the "firsts":
√12⋅√12=√144=12

Then the "outers":
√12⋅√2=√24

Then the "inners":
−√2⋅√12=−√24

Finally the "lasts":
−√2⋅√2=−√4=−2

When we combine these expressions we get:
12+√24−√24−2

The √24 and −√24 cancel each other out, so we're left with:
12−2

Which simplifies down to:
10

METHOD 2:

To solve this, we use:
enter image source here

This expression (√12−√2)(√12+√2) 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 a2−b2, so it becomes:
√122−√22

Simplify:
12−2

So the final answer is:
10

Hope this helps!

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
2982 views around the world
You can reuse this answer
Creative Commons License