SOLUTION: Please help... multiply and simplify (1 + square factor 3)^2 please show me how to work this out... Thank you

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Question 169711: Please help...
multiply and simplify
(1 + square factor 3)^2
please show me how to work this out...
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=sqrt%283%29

So the expression %281%2Bsqrt%283%29%29%5E2 becomes %281%2Bx%29%5E2




%281%2Bx%29%5E2 Start with the given expression.


%281%2Bx%29%281%2Bx%29 Expand. Remember something like A%5E2=A%2AA.


Now let's FOIL the expression.


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


%28highlight%281%29%2Bx%29%28highlight%281%29%2Bx%29 Multiply the First terms:%281%29%2A%281%29=1.


%28highlight%281%29%2Bx%29%281%2Bhighlight%28x%29%29 Multiply the Outer terms:%281%29%2A%28x%29=x.


%281%2Bhighlight%28x%29%29%28highlight%281%29%2Bx%29 Multiply the Inner terms:%28x%29%2A%281%29=x.


%281%2Bhighlight%28x%29%29%281%2Bhighlight%28x%29%29 Multiply the Last terms:%28x%29%2A%28x%29=x%5E2.


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1%2Bx%2Bx%2Bx%5E2 Now collect every term to make a single expression.


1%2B2%2Ax%2Bx%5E2 Now combine like terms.


So %281%2Bx%29%5E2 FOILs to 1%2B2%2Ax%2Bx%5E2.


In other words, %281%2Bx%29%5E2=1%2B2%2Ax%2Bx%5E2.



So %281%2Bsqrt%283%29%29%5E2=1%2B2%2Asqrt%283%29%2B%28sqrt%283%29%29%5E2



1%2B2%2Asqrt%283%29%2B%28sqrt%283%29%29%5E2 Start with the right side of the last equation


1%2B2%2Asqrt%283%29%2B3 Square sqrt%283%29 to get 3


4%2B2%2Asqrt%283%29 Combine like terms.



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Answer:


So %281%2Bsqrt%283%29%29%5E2=4%2B2%2Asqrt%283%29