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

Check it out:

Factor  8w^3 + 1

Rewrite it as cubes...

8w^3 + 1 = ( 2w )^3 + 1 = ( 2w + 1 ) ( ( 2w )^2 - ( 1 ) ( 2w ) + 1^2 ) = ( 2w + 1 ) ( 4w^2 - 2w + 1 )

Check it by multiplying!

Here's another one:

Factor    27x^3 + 64y^3

Rewrite it as cubes

27x^3 + 64y^3 = ( 3x )^3 + ( 4y )^3 = ( 3x + 4y ) ( ( 3x )^2 - ( 4y ) ( 3x ) + ( 4y )^2 ) = ( 3x + 4y ) ( 9x^2 - 12xy + 16y^2 )

YOUR TURN:

Factor  8a^3 + b^3

There is one more thing I need to tell you:

The ONLY place you'll ever see these cubed special guys is in math books!