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

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) (Show Source): You can put this solution on YOUR website!

Numerical example:
=
= and
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Algebraic Explanation:

Start with the given equation

FOIL the left side

Subtract from both sides. Subtract from both sides

Combine like terms

Case 1: Solving for "a"

Divide both sides by

Reduce

Or...

Case 2: Solving for "b"

Divide both sides by

Reduce

So is true only if "a" or "b" is 0 (or both are zero). Otherwise, the equation is false. So in general

Numerical Example:

Start with the given equation

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

Add

Square each term

Add

Since is not true, this means that we've just shown that is not true for all values of "a" and "b".

So once again, in general
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