Problem 52 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of \((x+2)^{3}\) is given by \(x^{3}+6x^{2}+12x+8\).

Step 1: Write down the given expression

The given expression is \((x+2)^{3}\).

Step 2: Apply the cubic identity

We apply the cubic identity to the given expression by substituting \(x\) for \(a\) and \(2\) for \(b\) in the identity \(a^{3}+3a^{2}b+3ab^{2}+b^{3}\). This gives us \(x^{3}+3x^{2}(2)+3x(2)^{2}+(2)^{3}\).

Step 3: Simplify the expression

Simplify the resultant equation to get the final answer. Perform all the multiplication operations in the expression we obtained in step 2 to get a simplified expression which is \(x^{3}+6x^{2}+12x+8\).