## Mathematical Mistakes

Though I am currently doing some history research, I thought it would be a nice idea to throw some mathematical myths out there for some people. There are plenty of myths or mistakes to go around, but a few of these should suffice. These reside in the algebra zone but apply elsewhere.

1. ax + b = a(x + b). An easy way to check this is to apply some values. a =2, x = 3 and b = 4. {2*3 +4 = 10} does not equal {2(3 + 4) = 14}.

2. a – (b + c) = a – b + c. Again, using a = 2, b = 3 and c = 4 you clearly see the mistake. {2-(3+4) = -10} does not equal {2 – 3 + 4 = 3}.

3.(a + b)^2 = a^2 + b^2. Apply the numbers and you see these do not equal.

4. (a – b)^2 = a^2 – b^2.

5. (a – b)/(c + b) = a/c

6. a(b + c)/(b + a) = (ac)/a = c

7. a/(b+c) = a/b + a/c I’ve seen my oldest make this mistake many times.

8. (ax + b)/(ac) = (x + b)/c

9. (a^x)(a^y) = a^(xy) Keep in mind ‘^’ means raised to the power.

10. a^(x+y) = a^x = a^y

These are but ten of the common mistakes students make. The easiest to double check yourself is to apply values to the variables and do the calculation.

It’s good using a couple quick tests to verify that some algebraic relationship is a mistake. There is the potential danger of happening to try a couple numbers which work, which would be a fluke but likely if you go looking in nice easy numbers.

I wonder if there’s a simple-to-remember, simple-to-calculate set of choices for a, b, c, x, and y that would break every one of these errors.

I don’t know. Seldom do I need to do these checks myself, so I never investigated it further than a test or two.