Factor 2x^4-32

Problem

2*x4−32

Solution

1. Factor out the greatest common factor, which is 2

2*(x4−16)

2. Identify the difference of squares pattern, a2−b2=(a−b)*(a+b) where a=x2 and b=4

2*((x2)2−4)

3. Apply the difference of squares formula to the expression inside the parentheses.

2*(x2−4)*(x2+4)

4. Identify another difference of squares in the factor (x2−4) where a=x and b=2

2*(x2−2)*(x2+4)

5. Apply the formula again to factor (x2−4) into (x−2)*(x+2)

2*(x−2)*(x+2)*(x2+4)

Final Answer

2*x4−32=2*(x−2)*(x+2)*(x2+4)

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