SOLUTION: Explain (a+b)^2 not equal to a^2 + b^2 give a numerial example to illustrate

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Question 153706: Explain (a+b)^2 not equal to a^2 + b^2
give a numerial example to illustrate
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2+%3C%3E+a%5E2%2Bb%5E2
Numerical example:
%285%2B7%29%5E2+=+%2812%29%5E2 = 144
5%5E2%2B7%5E2+=+25%2B49 = 74 and 144+%3C%3E+74

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Algebraic Explanation:

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


a%5E2%2B2ab%2Bb%5E2=a%5E2+%2B+b%5E2 FOIL the left side


2ab=a%5E2+%2B+b%5E2-a%5E2-b%5E2 Subtract a%5E2 from both sides. Subtract b%5E2 from both sides


2ab=0 Combine like terms


Case 1: Solving for "a"

a=0%2F%282b%29 Divide both sides by 2b


a=0 Reduce

Or...

Case 2: Solving for "b"


b=0%2F%282a%29 Divide both sides by 2b


b=0 Reduce


So %28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 is true only if "a" or "b" is 0 (or both are zero). Otherwise, the equation is false. So in general %28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2



Numerical Example:

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


%285%2B4%29%5E2=5%5E2%2B4%5E2 Plug in a=5 and b=4 (any two numbers will do as long as they are both not equal to zero)


%289%29%5E2=5%5E2%2B4%5E2 Add


81=25%2B16 Square each term


81=41 Add


Since 81=41 is not true, this means that we've just shown that %28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 is not true for all values of "a" and "b".

So once again, in general %28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2