Math is Fun
Bookmark Add to favorites
link Link here
Math is Fun HomeHome





Top-rated teacher Web sites rated by teacher usage
Edunet site of the week January 2001
Maths Is Fun is ICRA Registered

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 no Correction yes
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