Problem 41 - College Algebra

Question

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

Step-by-Step Solution

Answer

\((x+2)^{2}\) = \(x^{2} + 4x + 4\)

Step 1 Identify the components

In the expression \((x + 2)^2\), 'x' is 'a', '2' is 'b', and the exponent '2' is 'n'. So, our task is to apply the formula \((a+b)^2 = a^2 + 2ab + b^2\) to the expression.

Step 2 Apply the binomial theorem

By applying the expansion, we can substitute 'a' with 'x' and 'b' with '2' to the formula. This gives us \(a^2 + 2ab + b^2\) = \(x^2 + 2 * x * 2 + 2^2\). This simplifies to \(x^2 + 4x + 4\).

Step 3 Simplify the result

The final answer for the expanded form of \((x + 2)^2\) is \(x^2 + 4x + 4\). This is the expanded form of the given binomial equation.