SOLUTION: Explain in your own words(a+b)^2= a^2+b^2 Give a numerical example. Thank You

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Question 179563This question is from textbook
: Explain in your own words(a+b)^2= a^2+b^2
Give a numerical example. Thank You This question is from textbook

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