Factor u^4-1

Problem

u4−1

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.

u4−1=(u2)2−(1)2

3. Apply the formula for the difference of squares using a=u2 and b=1

u4−1=(u2−1)*(u2+1)

4. Identify that the first factor (u2−1) is also a difference of squares.

5. Apply the formula again to the factor (u2−1) using a=u and b=1

u2−1=(u−1)*(u+1)

6. Combine all factors to reach the final factored form.

u4−1=(u−1)*(u+1)*(u2+1)

Final Answer

u4−1=(u−1)*(u+1)*(u2+1)

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