Sure! Let's rewrite and simplify the expression [tex]\((2 + 6x)^2\)[/tex].
First, we will recall that [tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex]. In this case, [tex]\(a = 2\)[/tex] and [tex]\(b = 6x\)[/tex].
1. Square each term individually:
[tex]\[
(2)^2 = 4
\][/tex]
[tex]\[
(6x)^2 = (6^2)(x^2) = 36x^2
\][/tex]
2. Next, double the product of the two terms:
[tex]\[
2 \cdot 2 \cdot 6x = 24x
\][/tex]
3. Now, combine all the terms together:
[tex]\[
(2 + 6x)^2 = 4 + 24x + 36x^2
\][/tex]
After combining the terms, the simplified form of [tex]\((2 + 6x)^2\)[/tex] is:
[tex]\[
36x^2 + 24x + 4
\][/tex]
So, rewriting and simplifying the expression [tex]\((2 + 6x)^2\)[/tex] gives us:
[tex]\[
36x^2 + 24x + 4
\][/tex]
