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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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