Factor (x^2-1)^2

Problem

(x^2−1)^2

Solution

1. Identify the expression inside the square as a difference of squares, which follows the pattern a^2−b^2=(a−b)*(a+b)

2. Factor the inner expression x^2−1 by setting a=x and b=1

x^2−1=(x−1)*(x+1)

3. Apply the power of a product rule, which states (a*b)^n=a^n*b^n to the entire squared expression.

((x−1)*(x+1))^2=(x−1)^2*(x+1)^2

Final Answer

(x^2−1)^2=(x−1)^2*(x+1)^2

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