Factor x^4-256

Problem

x^4−256

Solution

1. Identify the expression as a difference of squares, noting that x^4=(x^2)^2 and 256=16^2

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

x^4−256=(x^2−16)*(x^2+16)

3. Identify that the first factor, x^2−16 is also a difference of squares because 16=4^2

4. Apply the formula again to the factor (x^2−16)

x^2−16=(x−4)*(x+4)

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

(x−4)*(x+4)*(x^2+16)

Final Answer

x^4−256=(x−4)*(x+4)*(x^2+16)

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