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

What about this guy?

x^2 + 4

What did we call special guy # 1 ?

The DIFFERENCE of two squares!

x^2+ 4  is a sum, not a difference... and we do NOT know how to factor him yet! ( Later!)

Special Guy # 2:

The difference of two cubes

x^3 - a^3 = ( x - a ) ( x^2 + ax + a^2 )

Memorize this puppy or you're dead meat on the test!

Check it out:

Factor  x^3 - 8

Rewrite it as cubes...

x^3 - 8 = x^3 - 2^3 = ( x - 2 ) ( x^2 + 2x + ( 2 )^2 ) = ( x - 2 ) ( x^2 + 2x + 4 )

Multiply it back out to check!