Let's evaluate each of the given expressions step-by-step to determine which one has a value of 21.
### Expression (A) [tex]$3 \cdot 2^2 + 12 \div 4$[/tex]
1. Evaluate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
2. Multiply by 3:
[tex]\[
3 \cdot 4 = 12
\][/tex]
3. Evaluate [tex]\(12 \div 4\)[/tex]:
[tex]\[
12 \div 4 = 3
\][/tex]
4. Add the results from steps 2 and 3:
[tex]\[
12 + 3 = 15
\][/tex]
### Expression (B) [tex]\((3 \cdot 2)^2 + 12 \div 4\)[/tex]
1. Multiply 3 by 2:
[tex]\[
3 \cdot 2 = 6
\][/tex]
2. Square the result:
[tex]\[
6^2 = 36
\][/tex]
3. Evaluate [tex]\(12 \div 4\)[/tex]:
[tex]\[
12 \div 4 = 3
\][/tex]
4. Add the results from steps 2 and 3:
[tex]\[
36 + 3 = 39
\][/tex]
### Expression (C) [tex]\(3 \cdot \left(2^2 + 12 \div 4\right)\)[/tex]
1. Evaluate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
2. Evaluate [tex]\(12 \div 4\)[/tex]:
[tex]\[
12 \div 4 = 3
\][/tex]
3. Add the results from steps 1 and 2:
[tex]\[
4 + 3 = 7
\][/tex]
4. Multiply by 3:
[tex]\[
3 \cdot 7 = 21
\][/tex]
### Expression (D) [tex]\(3 \cdot \left(2^2 + 12\right) \div 4\)[/tex]
1. Evaluate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
2. Add 12:
[tex]\[
4 + 12 = 16
\][/tex]
3. Multiply by 3:
[tex]\[
3 \cdot 16 = 48
\][/tex]
4. Divide by 4:
[tex]\[
48 \div 4 = 12
\][/tex]
From this evaluation, we can see that the expression in Choice (C) results in a value of 21.
Therefore, the expression that has a value of 21 is:
[tex]\[
\boxed{3 \cdot\left(2^2+12 \div 4\right)}
\][/tex]
