Problem 43 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of the binomial \((2x+3)^2\), when expanded, is \(4x^2 +12x +9\).

Step 1: Identify the Terms

Identify \(a\) and \(b\) in the expression \((2x+3)^2\). Here, \(a = 2x\) and \(b = 3\).

Step 2: Apply the Binomial Theorem

Use the binomial theorem, which states \((a + b)^2 = a^2 + 2ab + b^2\). Substituting \(a = 2x\) and \(b = 3\) we get, \((2x)^2 + 2*(2x)*(3) + (3)^2\).

Step 3: Simplify the Expression

Evaluate each of the terms separately. You get \(4x^2 +12x +9\)

Step 4: Write the Final Solution

Combine all of the terms to get the final solution, which is the expanded form of the binomial: \(4x^2 +12x +9\).