(a+b)2 = a2 + 2ab + b2
(a–b)2 = a2 – 2ab + b2
(a+b) (a–b) = a2 –b2
Note very carefully that (a+b)2 ≠ a2 + b2
and (a–b)2 ≠ a2 –b2. Do NOT do this!!!
Cancelling Fractions:
You can cancel factors out of the numerator and denominator of fractions only if the
same factor appears in every term in the numerator AND every term in the denominator
of the fraction.
2a  4b
a  2b

8c  12 d 4c  6d
2a  4b
8c  9d
cannot be simplified because the term 9d does not have a factor of 2 in it
2a  7 a 2  7 7


8a  5a 8  5 13
2a  7b
8a  5a
because each term in the original expression has a factor of 2 in it
because each term in the original expression has a factor of "a" in it
cannot be simplified because the term7b does not have a factor of "a" in it
The following are common mistakes. Do NOT do these!!
c 2  b 2 does not equal
c 2  b 2 does not equal
a
bc
does not equal
For example
1
1

23 5
c 2  b 2 . For example:
36  25  6  5  1
6 2  52  36  25  11 but 6  5  1
c-b For example:
a a

b c
36  25  11 but
You can not break up the denominator that way
1
2
1
3
is not the same as  
5
6