Simplify (x^2-1)^3

Problem

(x2−1)3

Solution

1. Identify the expression as a binomial cubed in the form (a−b)3 where a=x2 and b=1

2. Apply the formula for the cube of a binomial: (a−b)3=a3−3*a2*b+3*a*b2−b3

3. Substitute the values into the formula:

(x2)3−3*(x2)2*(1)+3*(x2)*(1)2−(1)3

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

x6−3*x4+3*x2−1

Final Answer

(x2−1)3=x6−3*x4+3*x2−1

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