Question 110148: Will somepne please help me solve this problem? fector completely: y^3-27
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You first need to realize that the problem is the difference of two cubes, i.e. the cube root of  is exactly y, and the cube root of 27 is exactly 3.
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The factorization of the difference of two cubes follows this pattern:
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So, substituting:
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Which is the final answer because neither of the factors can be factored any further. How can you tell? Look at the second factor, , then calculate  where a, b, and c are the coefficients of the first, second, and third terms -- in this case, they are 1, 3, and 9. In this case is a negative number. Anytime is negative or not a perfect square, then the expression cannot be factored.
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By the way, the sum of two cubes is factored as follows:
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