Factor x^4-16

Problem

x4−16

Solution

1. Identify the expression as a difference of squares, noting that x4=(x2)2 and 16=4

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

x4−16=(x2−4)*(x2+4)

3. Identify that the first factor, x2−4 is also a difference of squares because 4=2

4. Apply the formula again to the factor (x2−4) using a=x and b=2

x2−4=(x−2)*(x+2)

5. Combine all factors into the final expression, noting that x2+4 cannot be factored further using real numbers.

(x−2)*(x+2)*(x2+4)

Final Answer

x4−16=(x−2)*(x+2)*(x2+4)

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