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| Math Central | Quandaries & Queries |
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Question from Neji, a student: How do you factor (y-z) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2-yz+z^2) (y-z) (y^2+yz+z^2) as the answer? |
Neji,
Combining the first two factors as a difference of squares gives
(y2 - z2)(y4+y2z2+z4)
If you write a for y2 and b for z2 this is
(a - b)(a2 + ab + b2)
But this is a difference of cubes,
(a - b)(a2 + ab + b2) = (a3- b3) = (y6 - z6)
Next factor (y6 - z6) as a difference of squares.
Harley
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