In Exercise, factor by regrouping and using the distributive law (Example 1).x3 + 4x2 − 8x...

In Exercise, factor by regrouping and using the distributive law (Example 1).

x3 + 4x2 − 8x − 32

EXAMPLE 1

Factor:

(a) x6 − y6

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(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

 

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(b) Note that x8 = (x4)2 and let u = x4. Then

 

Observe that x4 = (x2)2 and let v = x2. Then