SOLUTION: x + 25^2=

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Question 574340: x + 25^2=
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
What you posted means:
x+%2B+25%2A25
since exponent only apply to what is right in front of it. And since 25 squared is 625 your expression simplifies to
x + 625

But I suspect that your problem is really:
%28x%2B25%29%5E2
Note the parentheses! They make a huge difference. In this expression it is the right parenthesis that is immediately in front of the exponent, not the 25. This means the exponent applies to the entire expression within the parentheses, not just the 25. So
%28x%2B25%29%5E2
is short for:
(x+25)(x+25)

To simplify this we can use FOIL:
x*x + x*25 + 25*x + 25*25
which simplifies as follows:
x%5E2+%2B25x+%2B+25x+%2B+625
x%5E2+%2B+50x+%2B+625

Instead of using FOIL we could have used the pattern:
%28a+%2B+b%29%5E2+=+a%5E2+%2B+2%2Aa%2Ab+%2B+b%5E2
with the "a" being "x" and the "b" being 25:
x%5E2+%2B+2%2Ax%2A25+%2B+25%5E2
which simplifies to
x%5E2+%2B+50x+%2B+625