Question 446207: Help please, I don't understand how to solve this, thank you I appreciate it.
Multiply
(2+ √5) (2-√5)
Found 2 solutions by Alan3354, Leaf W.:
Answer by Alan3354(69443)   (Show Source):
Answer by Leaf W.(135)  (Show Source):
You can put this solution on YOUR website! There are two ways to do this problem--one way is the long version, and one is a sort of shortcut. You will need to know the long way for other problems that are not as convenient, but the shortcut is extremely convenient and will save you much time.
Do you know how to multiply binomials using the FOIL method? That is the long version of solving it. In case you don't, here it is step by step.
1. Firsts--multiply the first number of each binomial--in this case, 2 and 2, so  = 4
2. Outers--multiply the two outer numbers of the entire expression--in this case, 2 and  , so  = 
3. Inners--multiply the two innermost numbers of the entire expression--in this case,  and 2, so  = 
4. Lasts--multiply the last number of each binomial--in this case,  and  , so  = -5 because the square root of 5 times the square root of 5 is 5, and one has a negative
==>Add your answers from steps 1-4: 4 +  + - 5
==>Combine like terms. Notice that + cancel each other out. 4 - 5 = -1. -1 is your final answer.
***SHORTCUT:
Just as with variable binomials, you can take a shortcut by not solving for the inner and outer numbers. This is because in all differences of squares--which are binomials that take the form (a + b)(a - b) =  --the values of the outers and innies are opposites and cancel each other out. In your case your 'a' is 2 and your 'b' is , so you can plug these values into : 
==>Multiply by the exponents: 4 - 5
==>Add like terms: -1
Therefore, your final answer is -1
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