SOLUTION: {{{(x+4)^2}}} and {{{x^2+16}}}. Can you tell me why they are not equal? I get the part when you say that they are different. But why are they? I have the answer to {{{(x+4)^2}}}, b

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: {{{(x+4)^2}}} and {{{x^2+16}}}. Can you tell me why they are not equal? I get the part when you say that they are different. But why are they? I have the answer to {{{(x+4)^2}}}, b      Log On


   

Question 495911: %28x%2B4%29%5E2 and x%5E2%2B16. Can you tell me why they are not equal? I get the part when you say that they are different. But why are they? I have the answer to %28x%2B4%29%5E2, but where is the solution to x%5E2%2B16? I am so confused.

Answer by kingme18(98) About Me  (Show Source):
You can put this solution on YOUR website!
These aren't equal because you can't distribute an exponent. When you raise something to the second power (square it), you're multiplying it by itself; thus, %28x%2B4%29%5E2 means %28x%2B4%29%28x%2B4%29. If you use FOIL to multiply, you get x%5E2+%2B+4x%2B+4x+%2B+16, or x%5E2%2B8x%2B16. When you just distribute the exponent, you lose that middle "+8x" term, which is why %28x%2B4%29%5E2 and x%5E2%2B16 are not equal.

I'm not sure what you mean about the solution to x%5E2%2B16. That is already simplified; it's just not the same as %28x%2B4%29%5E2, which is x%5E2%2B8x%2B16.