Simplify (x^2-1)^3

Problem

(x^2−1)^3

Solution

1. Identify the expression as a binomial cubed in the form (a−b)^3 where a=x^2 and b=1

2. Apply the formula for the cube of a binomial: (a−b)^3=a^3−3*a^2*b+3*a*b^2−b^3

3. Substitute the values into the formula:

(x^2)^3−3*(x^2)^2*(1)+3*(x^2)*(1)^2−(1)^3

4. Simplify each term using the power of a power rule (x^m)^n=x^(m*n)

x^6−3*x^4+3*x^2−1

Final Answer

(x^2−1)^3=x^6−3*x^4+3*x^2−1

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