To evaluate the expression [tex]\(3x^2 + 4(x + 2x) + 10\)[/tex] when [tex]\(x = 2\)[/tex], let's break it down step-by-step:
1. Substitute [tex]\(x = 2\)[/tex]:
We substitute [tex]\(x\)[/tex] with 2 in the given expression:
[tex]\[
3(2)^2 + 4(2 + 2 \cdot 2) + 10
\][/tex]
2. Evaluate each term:
- First term: [tex]\(3(2)^2\)[/tex]
[tex]\[
3 \cdot 4 = 12
\][/tex]
So, the first term evaluates to 12.
- Second term: [tex]\(4(2 + 2 \cdot 2)\)[/tex]
[tex]\[
2 \cdot 2 = 4 \\
2 + 4 = 6 \\
4 \cdot 6 = 24
\][/tex]
So, the second term evaluates to 24.
- Third term: [tex]\(10\)[/tex]
- This is already given as a constant term and remains 10.
3. Sum all the terms:
Let's add the results from the evaluated terms:
[tex]\[
12 + 24 + 10 = 46
\][/tex]
So, the value of the expression [tex]\(3x^2 + 4(x + 2x) + 10\)[/tex] when [tex]\(x = 2\)[/tex] is 46.
Therefore, the final evaluated result is:
[tex]\[
\boxed{46}
\][/tex]
