Basic Algebra/Factoring/Factoring a^2-b^2 Binomials
Difference of Squares
Any binomial of the form may be written as . That is
Example 1: Factor .
This is clearly seen just take and so that . So
Example 2:: .
Here it is unclear where we can use the difference of squares as 32 is NOT a perfect square. However if we look we see that we can factor out a common factor of 2.
Now we see we can use the difference of two squares to simplify matters take and :
Now we notice that we can use the difference of squares again in the first factor to get:
This is now completely factored.
This is brings us to our next point that is that is NOT FACTORABLE (at least for the purposes of this class).
Let a = b
Therefore: a^2 = ab
Therefore: a^2 - b^2 = ab - b^2
Therefore: (a + b)(a - b) = b(a - b)
Now divide both sides by (a - b)
Therefore: a + b = b
But since a = b and substituting b for a
Therefore: b + b = b
Therefore: 2b = b
Now divide both sides by b
Therefore: 2 = 1