Question

For all real numbers a and b, 2a • b = a2 + b2. True or False ? Explain.

Answer 1

False. You can pick any two numbers, but not the same number, to show its false. try it

Answer 2

First step of the equation is to simplify the equation 2a • b = a2 + b2 into 2 ab =  a2 + b2. This cannot be factored anymore although. when we try to substitute a with 5 and b with 2, the answer in the right hand side of the equation is -9. hence the answer to this problem is false. we can try another values to verify