SOLUTION: ( sqrt 5 - sqrt7)^2 answer:12 - 2 sqrt 35 ok so i tried the foil method and i got sqrt 5 sqrt7 as my answer can anyone tell me how my book got 12-2 sqrt 35 as an ans

Algebra ->  Signed-numbers -> SOLUTION: ( sqrt 5 - sqrt7)^2 answer:12 - 2 sqrt 35 ok so i tried the foil method and i got sqrt 5 sqrt7 as my answer can anyone tell me how my book got 12-2 sqrt 35 as an ans      Log On


   

Question 195531: ( sqrt 5 - sqrt7)^2


answer:12 - 2 sqrt 35

ok so i tried the foil method and i got sqrt 5 sqrt7 as my answer can anyone tell me how my book got 12-2 sqrt 35 as an answer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28sqrt%285%29-sqrt%287%29%29%5E2 Start with the given expression.


%28sqrt%285%29-sqrt%287%29%29%28sqrt%285%29-sqrt%287%29%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28sqrt%285%29%29-sqrt%287%29%29%28highlight%28sqrt%285%29%29-sqrt%287%29%29 Multiply the First terms:%28sqrt%285%29%29%2A%28sqrt%285%29%29=sqrt%285%2A5%29=sqrt%2825%29=5.


%28highlight%28sqrt%285%29%29-sqrt%287%29%29%28sqrt%285%29%2Bhighlight%28-sqrt%287%29%29%29 Multiply the Outer terms:%28sqrt%285%29%29%2A%28-sqrt%287%29%29=-sqrt%285%2A7%29=-sqrt%2835%29.


%28sqrt%285%29%2Bhighlight%28-sqrt%287%29%29%29%28highlight%28sqrt%285%29%29-sqrt%287%29%29 Multiply the Inner terms:%28-sqrt%287%29%29%2A%28sqrt%285%29%29=-sqrt%287%2A5%29=-sqrt%2835%29.


Multiply the Last terms:%28-sqrt%287%29%29%2A%28-sqrt%287%29%29=sqrt%287%2A7%29=sqrt%2849%29=7.


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So we have the terms: 5, -sqrt%2835%29, -sqrt%2835%29, and 7


5-sqrt%2835%29-sqrt%2835%29%2B7 Now add every term listed above to make a single expression.


12-2%2Asqrt%2835%29 Now combine like terms.


So %28sqrt%285%29-sqrt%287%29%29%5E2 FOILs to 12-2%2Asqrt%2835%29.


In other words, %28sqrt%285%29-sqrt%287%29%29%5E2=12-2%2Asqrt%2835%29.