Factor x^4-1

Problem

x4−1

Solution

1. Identify the expression as a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

2. Rewrite the terms as squares to match the pattern.

x4−1=(x2)2−1

3. Apply the formula for the difference of squares using a=x2 and b=1

x4−1=(x2−1)*(x2+1)

4. Identify that the first factor (x2−1) is also a difference of squares.

5. Apply the formula again to the factor (x2−1) using a=x and b=1

x2−1=(x−1)*(x+1)

6. Combine all factors into the final expression.

x4−1=(x−1)*(x+1)*(x2+1)

Final Answer

x4−1=(x−1)*(x+1)*(x2+1)

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