From the sum fo `5a^(2)b - 7 ab + 10 " and " -3a^(2)b + 3ab - 4`, subtract 6ab + 15.

Options

A. `2a^(2)b + 2ab - 9`
B. `2a^(2)b -4ab +6`
C. `2a^(2)b - 10ab -9`
D. `5a^(2)b - 2ab - 9`

Answer

To solve the problem step by step, we will first find the sum of the two algebraic expressions and then subtract the third expression from that sum.

### Step 1: Find the sum of the two expressions
We have the two expressions:
1. \(5a^2b - 7ab + 10\)
2. \(-3a^2b + 3ab - 4\)

We will add these two expressions together.

\[ (5a^2b - 7ab + 10) + (-3a^2b + 3ab - 4) \]

### Step 2: Combine like terms
Now, we will combine the like terms:

- Combine \(a^2b\) terms:
\(5a^2b - 3a^2b = 2a^2b\)

- Combine \(ab\) terms:
\(-7ab + 3ab = -4ab\)

- Combine constant terms:
\(10 - 4 = 6\)

So, the sum of the two expressions is:
\[ 2a^2b - 4ab + 6 \]

### Step 3: Subtract the third expression
Now we need to subtract the expression \(6ab + 15\) from the result we obtained in Step 2.

\[ (2a^2b - 4ab + 6) - (6ab + 15) \]

### Step 4: Distribute the negative sign
Distributing the negative sign gives us:
\[ 2a^2b - 4ab + 6 - 6ab - 15 \]

### Step 5: Combine like terms again
Now we will combine the like terms again:

- The \(a^2b\) term remains:
\(2a^2b\)

- Combine \(ab\) terms:
\(-4ab - 6ab = -10ab\)

- Combine constant terms:
\(6 - 15 = -9\)

So, the final expression after subtraction is:
\[ 2a^2b - 10ab - 9 \]

### Final Answer
The final answer is:
\[ 2a^2b - 10ab - 9 \]

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