Top 10 errors in algebra

By | April 4, 2011

Mathematics is indeed a universal language. Even errors are universal. Here are the top ten errors in algebra which are beyond borders and colors.

#10. Squaring the negative. A minus a squared unless it’s been snared: $-8^2\neq 64$

#09. Logarithms: The log of the sum ain’t the sum of the log: $\log(a+b)\neq\log_a+log_b$

#08. Shifting function: Add to y go high, add to x go west: $y = (x+3)^2$

#07. Inequality: Multiplying the inequality by a negative flips the inequality: $-3(x<5) \neq -3x<-15$

#06. On exponents: When in doubt, write it out: $x^4 = x.x.x.x$

#05. Fractional exponent: Don’t flip over the root. $25^{\frac{1}{2}} \neq \frac{1}{25^2}$

#04. Subtraction: Don’t forget to share the minus and the negativity. $x-(3+x) \neq x-3+x$

#03. Cancellation: Cancel factors, not individual terms. $\frac {x}{x-5} \neq \frac{1}{-5}$

#02. Quadratics: Remember exponents 2, answers 2. $x^2=25, x=5, x=-5$

#01. Squaring: Don’t forget to FOIL. $(x-3)^2 \neq x^2 -9$.

Here is a funny video of common algebra mistakes listed above:

Here is one comment from YouTube viewer:

For all the idiots who say #10 and #2 contradict themselves are completely wrong.#10:-8^2 IS NOT (-8)^2. Without the parenthesis, -8^2 = (-1)(8)(8), which equals -64. Do you guys see it now? (-8)^2 = (-8)(-8) = 64, which is 100% correct. I see where you guys are coming from, but thats why its a top 10 mistake.#2:5*5 = 25, -5 * -5 = 25. What’s wrong? How does this contradict #10?

Do you agree? How would you explain to students that $-8^2\neq 64$ when they know that $-8$ is the negative number 8?

1. Noah