Simplify (x-4)^3

Problem

(x−4)^3

Solution

1. Identify the expression as a binomial cube of the form (a−b)^3

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

3. Substitute a=x and b=4 into the formula.

4. Expand the terms: x^3−3*(x^2)*(4)+3*(x)*(4^2)−4^3

5. Simplify each term by performing the multiplication and exponentiation.

6. Calculate the final coefficients: x^3−12*x^2+3*(x)*(16)−64

7. Combine all parts to reach the final polynomial form.

Final Answer

(x−4)^3=x^3−12*x^2+48*x−64

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