Problem 44 - College Algebra

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: Identify the elements of the binomial

In the binomial \((3x+2)^{2}\), the elements are \(3x\) (which is 'a') and \(2\) (which is 'b').

Step 2: Apply the binomial expansion formula

Substitute the values of 'a' and 'b' into the formula \((a+b)^2= a^2+2ab+b^2\), which gives \((3x+2)^2= (3x)^2+2*(3x)*2+(2)^2\).

Step 3: Simplify the equation

Further simplify the equation to \((3x+2)^2= 9x^2+12x+4\).