Certainly! Let's expand the expression \((2x + 3)^2\) step-by-step.
First, recognize that \((2x + 3)^2\) means \((2x + 3) \cdot (2x + 3)\).
Using the distributive property (also known as the FOIL method for binomials), we expand this product:
1. First: Multiply the first terms of each binomial:
[tex]\[
2x \cdot 2x = 4x^2
\][/tex]
2. Outer: Multiply the outer terms of the expression:
[tex]\[
2x \cdot 3 = 6x
\][/tex]
3. Inner: Multiply the inner terms of the expression:
[tex]\[
3 \cdot 2x = 6x
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
3 \cdot 3 = 9
\][/tex]
Next, combine all these results together:
[tex]\[
4x^2 + 6x + 6x + 9
\][/tex]
Combine the like terms \(6x + 6x\):
[tex]\[
4x^2 + 12x + 9
\][/tex]
Therefore, the expanded form of \((2x + 3)^2\) is:
[tex]\[
4x^2 + 12x + 9
\][/tex]
So, we can fill in the blanks as follows:
[tex]\[
(2x + 3)^2 = 4x^2 + 12x + 9
\][/tex]
