SOLUTION: (a+b)^2= a^2+b^2 Explain in the following in your own words. Give numerical example to illustrate. Please help. Thanks!

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Question 179515This question is from textbook Elementary and Intermediate Algebra Concepts and Applications
: (a+b)^2= a^2+b^2
Explain in the following in your own words. Give numerical example to illustrate. Please help. Thanks! This question is from textbook Elementary and Intermediate Algebra Concepts and Applications

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 is NOT true in general, here's why:


%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 Start with the given equation.


a%5E2%2B2ab%2Bb%5E2=+a%5E2%2Bb%5E2 FOIL


Subtract a%5E2 from both sides. Subtract b%5E2 from both sides. Notice how the a%5E2 and the b%5E2 terms cancel out.


2ab=0 Simplify


a=0 or b=0 Set each individual factor equal to zero


So %28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 is only true if a=0 or b=0 (or both are zero). However, for any other values of "a" and "b", %28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 is NOT true.



Here's an example to support the answer:


%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 Start with the given equation.


%282%2B3%29%5E2=2%5E2%2B3%5E2 Plug in a=2 and b=3 (just pick 2 random values. Make sure that both are nonzero values)


5%5E2=2%5E2%2B3%5E2 Add


5%5E2=4%2B3%5E2 Square 2 to get 4


5%5E2=4%2B9 Square 3 to get 9


25=4%2B9 Square 5 to get 25


25=13 Add


Since 25%3C%3E13, this means that we've just shown an example where %28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 is not true. So %28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 is not true in general