Factor 81x^4-1

Problem

81*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 find a and b

81*x4=(9*x2)2

1=1

3. Apply the formula for the difference of squares using a=9*x2 and b=1

81*x4−1=(9*x2−1)*(9*x2+1)

4. Identify that the first factor (9*x2−1) is also a difference of squares.

9*x2=(3*x)2

1=1

5. Apply the formula again to the factor (9*x2−1) using a=3*x and b=1

9*x2−1=(3*x−1)*(3*x+1)

6. Combine all factors into the final expression.

Final Answer

81*x4−1=(3*x−1)*(3*x+1)*(9*x2+1)

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