Subtract `3a^2-5a+6b-8` from `2a^2+4a+7ab+1`

Answer

To solve the problem of subtracting \(3a^2 - 5a + 6b - 8\) from \(2a^2 + 4a + 7ab + 1\), we can follow these steps:

### Step 1: Write the expression for subtraction
We need to subtract \(3a^2 - 5a + 6b - 8\) from \(2a^2 + 4a + 7ab + 1\). This can be expressed as:
\[ (2a^2 + 4a + 7ab + 1) - (3a^2 - 5a + 6b - 8) \]

### Step 2: Distribute the negative sign
When we subtract the second expression, we need to distribute the negative sign across all the terms:
\[ 2a^2 + 4a + 7ab + 1 - 3a^2 + 5a - 6b + 8 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- For \(a^2\) terms: \(2a^2 - 3a^2 = -1a^2\)
- For \(a\) terms: \(4a + 5a = 9a\)
- For \(b\) terms: \(7ab - 6b\) (this remains as is since they are not like terms)
- For constant terms: \(1 + 8 = 9\)

Putting it all together, we have:
\[ -1a^2 + 9a + 7ab - 6b + 9 \]

### Step 4: Write the final answer
Thus, the final result of the subtraction is:
\[ -a^2 + 9a + 7ab - 6b + 9 \]