SOLUTION: Hi! I was wondering: Does [B^2 + A^2] = [(A+B)^2]? Why or why not? I've tried proving this with numerous numbers, and it only works when either A or B is zero. On my homework,

Question 279759: Hi! I was wondering:
Does [B^2 + A^2] = [(A+B)^2]? Why or why not? I've tried proving this with numerous numbers, and it only works when either A or B is zero. On my homework, I have to say why or why not this equation is true, and prove or disprove it with algebra. I don't get it?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
It is not true. So in general. To show that it is false, simply find values of A and B which contradict the equation.

By the way, the only solutions to are when either or . If , then which then becomes which is true for all B. This argument works similarly when . For any other values of A and B, the equation is false.

Here's why the only solutions are or :

Start with the given equation.

FOIL

Subtract from both sides. Subtract from both sides.

Rearrange the equation.

Divide both sides by 2.

or Use the zero product property.
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