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Top 10 errors in algebra

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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?

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