`(5jk^(2)+5j^(2)-5j^(2)k)-(jk^(2)+2j^(2)k+5j^(2))`
Which of the following is equivalent to the expressions above?

Options

A. `4jk^(2)`
B. `4jk^(2)-7j^(2)k`
C. `5j^(2)k^(4)-10j^(2)k`
D. `8j^(2)k^(3)+7j^(2)k-5j^(2)`

Answer

To solve the expression \((5jk^{2}+5j^{2}-5j^{2}k)-(jk^{2}+2j^{2}k+5j^{2})\), we will follow these steps:

### Step 1: Distribute the negative sign
We need to distribute the negative sign across the second set of parentheses. This means we will change the signs of each term inside the parentheses.

\[ (5jk^{2} + 5j^{2} - 5j^{2}k) - (jk^{2} + 2j^{2}k + 5j^{2}) \]

becomes:

\[ 5jk^{2} + 5j^{2} - 5j^{2}k - jk^{2} - 2j^{2}k - 5j^{2} \]

### Step 2: Combine like terms
Now we will combine the like terms. We will group the terms based on their variables:

- For \(jk^{2}\): \(5jk^{2} - jk^{2}\)
- For \(j^{2}\): \(5j^{2} - 5j^{2}\)
- For \(j^{2}k\): \(-5j^{2}k - 2j^{2}k\)

Now, let's simplify each group:

1. \(5jk^{2} - jk^{2} = (5 - 1)jk^{2} = 4jk^{2}\)
2. \(5j^{2} - 5j^{2} = 0\)
3. \(-5j^{2}k - 2j^{2}k = (-5 - 2)j^{2}k = -7j^{2}k\)

### Step 3: Write the final expression
Now, we can write the final expression by combining the results from the previous step:

\[ 4jk^{2} + 0 - 7j^{2}k = 4jk^{2} - 7j^{2}k \]

Thus, the expression simplifies to:

\[ 4jk^{2} - 7j^{2}k \]

### Conclusion
The equivalent expression is \(4jk^{2} - 7j^{2}k\).

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