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Special Guys (Difference of Two Squares, Sum and Difference of Two Cubes)

Special Guy # 1:

The difference of two squares

x^2 - a^2 = ( x - a ) ( x + a ) ... difference of squares equation

Check it out:

Factor   x^2 - 9

Write it as

x^2 - 3^2 ... the 3 is the a in the difference of squares equation

x^2 - 9 = x^2 - 3^2 = ( x - 3 ) ( x + 3 )

Check using FOIL -- Believe me?

TRY IT:

Factor
 		y^2 - 16
 

Here's another one:

Factor   25b^2 - 1

Rewrite it as squares...

25b^2 - 1 ... the 25b^2 becomes 5 * 5 * b * b ... which gives ( 5b ) ^2 - 1^2 = ( 5b - 1 ) ( 5b + 1 )

YOUR TURN:

Factor  4x^2 - 81