Add to favorites Link here
Home

Copyright © 2010
MathsIsFun.com

# Algebra Mistakes

I have gathered here a collection of mistakes that are pretty easy to make.

Try to avoid these!

Mistake Correction
x2 = 25, so x = 5 x = 5 or x= -5
(x-5)2 = x2 - 25 = (x-5)(x-5) = x2 - 10x + 25
√(x2+y2) = x + y √(x2+y2) is as far as you can go

x2x4 = x8 = x6 (add exponents)
(x2)4 = x6 = x8 (multiply exponents)
2x-1 = 1/(2x) = 2/x
-52 = 25 = -25 (do exponent before minus)
(-5)2 = -25 = +25 (do brackets before exponent)
5½ = 1/52 = √5

log(a+b) = log(a) + log(b) log(a+b) is as far as you can go

x(a/b) = xa/xb = xa/b
x-(5+a) = x-5+a = x-5-a

Here are some more mistakes in detail:

## Square root of xy

√(xy) =√x√y ... but not always!

### Example: x = -5 and y = -2

 √10 = √(-5×-2) = √(-5)√(-2) (The mistake) = i√5 × i√2 = i2√5√2 = - √10

So ... √10 = - √10 ??? I think not!

√(xy) =√x√y only when x and y are both >= 0

## Two Equals One

### Example:

 x = y Multiply both sides by x: x2 = xy Subtract y2 from both sides: x2 - y2 = xy - y2 Factor: (x+y)(x-y) = y(x-y) Divide both sides by (x-y): x + y = y (The mistake) Since x = y, we see that 2y = y Thus 2 = 1

Why is that wrong? Silly person! You tried to divide by zero.

Remember we said that x=y, so (x-y)=0 and going from (x+y)(x-y) = y(x-y) to x + y = y is a mistake.

## Factoring

### Example: Solve x2 – 5x = 2

 x2 – 5x = 2 Factor x: x(x-5) = 2 So: x=2 or x-5=2 (The mistake) Hence x=2 or 7

That would only work when x(x-5) = 0