Let's simplify the given expression step-by-step:
[tex]\[ 3(7mn + 3k) + 2(5k - 2mn) \][/tex]
1. Distributing the constants inside the parentheses:
- First distribute [tex]\(3\)[/tex] into [tex]\(7mn + 3k\)[/tex]:
[tex]\[
3(7mn) + 3(3k) = 21mn + 9k
\][/tex]
- Next, distribute [tex]\(2\)[/tex] into [tex]\(5k - 2mn\)[/tex]:
[tex]\[
2(5k) - 2(2mn) = 10k - 4mn
\][/tex]
2. Combining the terms:
Collect the terms obtained from the distribution:
[tex]\[
21mn + 9k + 10k - 4mn
\][/tex]
3. Combine the like terms:
- Combine the [tex]\(mn\)[/tex] terms:
[tex]\[
21mn - 4mn = 17mn
\][/tex]
- Combine the [tex]\(k\)[/tex] terms:
[tex]\[
9k + 10k = 19k
\][/tex]
4. Write the final simplified expression:
[tex]\[
17mn + 19k
\][/tex]
So, the final expression simplifies to:
[tex]\[
17mn + 19k
\][/tex]
Therefore, the correct answer is:
B [tex]\(17mn + 19k\)[/tex]
