To expand the expression [tex]\((3 + m)^2\)[/tex], we can use the binomial theorem. The binomial theorem states that:
[tex]\[
(a + b)^2 = a^2 + 2ab + b^2
\][/tex]
In this specific case, [tex]\(a = 3\)[/tex] and [tex]\(b = m\)[/tex]. Let's substitute these values into the binomial theorem:
[tex]\[
(3 + m)^2 = (3)^2 + 2 \cdot 3 \cdot m + (m)^2
\][/tex]
Now, we can calculate each term separately:
1. [tex]\(3^2 = 9\)[/tex]
2. [tex]\(2 \cdot 3 \cdot m = 6m\)[/tex]
3. [tex]\(m^2\)[/tex]
Putting these all together, we get:
[tex]\[
(3 + m)^2 = 9 + 6m + m^2
\][/tex]
So, the expanded form of [tex]\((3 + m)^2\)[/tex] is:
[tex]\[
9 + 6m + m^2
\][/tex]
