Problem 42 - College Algebra

Question

Find each product. $$(x+5)^{2}$$

Step-by-Step Solution

Answer

Hence, the product of the given expression \((x + 5)^2\) is \(x^2 + 10x + 25\).

Step 1: Identify the binomial expression

The binomial expression given is \((x + 5)^2\).

Step 2: Apply the formula

Apply the special expansion formula for \((x + a)^2\), which is \((x + a)^2 = x^2 + 2ax + a^2\). Here, \(a=5\). Substituting these values into the formula gives \(x^2 + 2(5)x + (5)^2\).

Step 3: Simplify the expression

Simplify \(2(5)x\) and \((5)^2\) to get \(10x\) and \(25\) respectively. Therefore, the expanded and simplified expression is \(x^2 + 10x + 25\).