Problem 42 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product of the binomial (x + 5) squared is \(x^2 + 10x + 25\).

Step 1: Understand the formula

Recognize that this problem is applying the formula for the square of a binomial. The formula is \((a+b)^2 = a^2 + 2ab + b^2\). In our case, 'a' is 'x' and 'b' is '5'.

Step 2: Apply the formula

Apply the formula \((a+b)^2 = a^2 + 2ab + b^2\) to get the product of the square of the binomial. Here, 'a' is 'x' and 'b' is '5'. \[(x+5)^2 = (x)^2 + 2*(x)*(5) + (5)^2\]

Step 3: Simplify

Simplify the expression to find the product. \[(x)^2 + 2*(x)*(5) + (5)^2 = x^2 + 10x + 25\]