Problem 52 - College Algebra Essentials

Question

Find each product. $$(x+2)^{3}$$

Step-by-Step Solution

Answer

\((x+2)^{3}\) expands to \(x^3 + 6x^2 + 12x + 8\).

Step 1: Expand the Expression

\((x+2)^{3}\) can be written as \((x+2) * (x+2) * (x+2)\). Let's expand this step by step. First, we expand the first two brackets: \((x+2) * (x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4\).

Step 2: Multiply with Third Bracket

Now, the result \((x^2 + 4x + 4)\) is multiplied with the third bracket \((x+2)\). This gives us: \(x^3 + 4x^2 + 4x + 2x^2 + 8x + 8 + 2x^3 + 8x^2 + 8x = x^3 + 6x^2 + 12x + 8\).