Problem 55 - College Algebra

Question

Find each product. $$(x-3)^{3}$$

Step-by-Step Solution

Answer

The solution to \( (x - 3)^3 \) is \( x^3 - 9x^2 + 27x - 27 \).

Step 1: Identify the binomial and cube power

In this exercise, the binomial is \( (x - 3) \) and the power is 3. This means that we will cube the binomial \( (x - 3) \).

Step 2: Apply the cubic formula of binomial

The standard equation of the cubic power of a binomial \( (a - b)^3 \) is given by \( a^3 - 3a^2b + 3ab^2 - b^3 \). In this exercise, \( a \) corresponds to \( x \) and \( b \) corresponds to 3. Substituting these values into the standard formula, we get: \( x^3 - 3* x^2*3 + 3* x*3^2 - 3^3 \).

Step 3: Simplify the equation

After substituting the values from Step 2, now the task is to simplify the equation. So starting with \( x^3 - 3* x^2*3 + 3* x*3^2 - 3^3 \), this equation simplifies to \( x^3 - 9x^2 + 27x - 27 \).