Factor a^4-1

Problem

a4−1

Solution

1. Identify the expression as a difference of squares, which follows the pattern x2−y2=(x−y)*(x+y)

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

a4−1=(a2)2−(1)2

3. Apply the formula for the difference of squares using x=a2 and y=1

(a2)2−(1)2=(a2−1)*(a2+1)

4. Identify that the first factor (a2−1) is also a difference of squares.

5. Apply the formula again to the factor (a2−1)

a2−1=(a−1)*(a+1)

6. Combine all factors into the final expression.

(a−1)*(a+1)*(a2+1)

Final Answer

a4−1=(a−1)*(a+1)*(a2+1)

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