Problem 44 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product of \( (3x + 2)^2 \) is \( 9x^2 + 12x + 4 \).

Step 1: Expand the Square

Expand the expression \( (3x + 2)^2 \) into \( (3x + 2) * (3x + 2) \)

Step 2: Distribute the terms

Distribute the terms: Multiply each term in the first parentheses by each term in the other parentheses. This leads to: \( (3x * 3x) + (3x * 2) + (2 * 3x) + (2 * 2) \)

Step 3: Simplify the terms

Simplify each of the terms: \( 9x^2 + 6x + 6x + 4 \)

Step 4: Combine like terms

Now, combine like terms: \( 9x^2 + 12x + 4 \)