In Exercise, factor by regrouping and using the distributive law (Example 1).
u2v − 2w2 − 2uvw + uw
EXAMPLE 1
Factor:
(a) x6 − y6
(b) x8 − 1.
SOLUTION
Once again, we want to put each polynomial in quadratic form.
(a) Note that x6 = (x3)2 and y6 = (y3)2. Let u = x3 and v = y3. Then
(b) Note that x8 = (x4)2 and let u = x4. Then
Observe that x4 = (x2)2 and let v = x2. Then
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