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

Here's another one:

Factor     27y^3 - 64

Rewrite it as cubes:

27y^3- 64 = ( 3y )^3 - 4^3 = ( 3y - 4 ) ( ( 3y )^2 + ( 4 ) ( 3y ) + ( 4 )^2 ) = ( 3y - 4 ) ( 9y^2 + 12y + 16 ) ... by the way, the trinomial in the final answer will never factor. NEVER!

TRY IT:

Factor   125x^3 - 1

Special Guy # 3:

The sum of two cubes

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

Know it. Love it.