SOLUTION: Explain the following in your own words: (a + b)2 a2 + b2. Give a numerical example to illustrate this.

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Question 154087: Explain the following in your own words: (a + b)2 a2 + b2. Give a numerical example to illustrate this.
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