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Sums and Differences of Cubes (and other odd powers)?
You can factor a sum or difference of cubes using the formulasa3 - b 3 = (a - b )(a2 + ab + b2)anda3 + b3 = (a + b)(a2 - ab + b2).For example, y3 + 8= y3 + 23= (y + 2)(y2 -2y + 4).Here's another example:x6 - 27 =(x2 ) 3 - 33 =(x2 -3 ) ((x2) 2 +3x2 + 9)
= (x2 -3 )(x4 + 3x2 + 9).
How do you know if a monomial is a perfect cube? It's easy. It's a cube if
1. The coefficient is a perfect cube (it can be positive or negative); 2. All the exponents on the variables are multiples of 3.
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