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

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) (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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