SOLUTION: Factor the sum or difference of two cubes. z^3+64

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Question 637375: Factor the sum or difference of two cubes.
z^3+64
Found 2 solutions by DrBeeee, Alan3354:
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
z^3 + 64 = 0 or
z^3 = -64
Because this is a third order equation it has 3 roots. The obvious real root is z = -4 which gives the factor
(z + 4)
To find the other factors simply divide z + 4 into the given equation
(z^3+64)/(z+4) = z^2 - 4z + 16
The resulting quadratic has a pair of complex roots:
z = 4 at an angle of +/- 60 degrees
The factors of z^3+64 are in polar form
(z+4)(z+4@60 degrees)(z+4@-60 degrees) or in quadrature form
(z+4)(z-2*(1+i*sqrt(3)))(z-2*(1-i*sqrt(3)))

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the sum or difference of two cubes.
z^3+64
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a%5E3+%2B+b%5E3+=+%28a%2Bb%29%2A%28a%5E2+-+ab+%2B+b%5E2%29
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a%5E3+-+b%5E3+=+%28a-b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29
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I recommend you remember those 2.