SOLUTION: s2-10st+25t2. m2-16n2. 5x2-125y2.

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Question 701163: s2-10st+25t2.
m2-16n2.
5x2-125y2.

Answer by Simnepi(216) About Me  (Show Source):
You can put this solution on YOUR website!
s%5E2-10st%2B25t%5E2 from the binomial theorem we know that %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2
Comparing the equations we see that a%5E2=s%5E2 therefore a=s (by taking the square root of both sides)
Also we see that
b%5E2=25t%5E2 from this we deduce that b=5t .
giving s%5E2-10st%2B25t%5E2=%28s-5t%29%5E2
next
m%5E2-16n%5E2 again, using the binomial theorem we know that %28a%2Bb%29%28a-b%29=a%5E2-b%5E2
Comparing the equations we see that a%5E2=m%5E2 therefore a=m.
Also we see that
b%5E2=16n%5E2 again, we can take the square root of both sides to find b=4n
Giving m%5E2-16n%5E2=%28m%2B4n%29%28m-4n%29
next
5x%5E2-125y%5E2 let's look for a common factor! Both terms can be divided by 5 so lets take that out.
5%28x%5E2-25y%5E2%29Now this looking like in the second problem.
using the binomial theorem we know that %28a%2Bb%29%28a-b%29=a%5E2-b%5E2
Comparing the equations a%5E2=x%5E2 giving a=x
and b%5E2=25y%5E2 from which we deduce b=5y
This gives
5x%5E2-125y%5E2=5%28x%2B5y%29%28x-5y%29