Factor x^4-256

Problem

x4−256

Solution

1. Identify the expression as a difference of squares, noting that x4=(x2)2 and 256=16

2. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=x2 and b=16

x4−256=(x2−16)*(x2+16)

3. Identify that the first factor, x2−16 is also a difference of squares because 16=4

4. Apply the formula again to the factor (x2−16)

x2−16=(x−4)*(x+4)

5. Combine all factors to write the completely factored expression.

(x−4)*(x+4)*(x2+16)

Final Answer

x4−256=(x−4)*(x+4)*(x2+16)

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