-2a²+3a-6.
To find this solution, we need to follow the steps of subtracting polynomials:
1. First, write out the two expressions horizontally, ensuring that like terms (terms with the same variable and power) line up vertically.
a²+a-1
3a²-2a+5
2. Second, change all the signs of the second line. That's because when we subtract, we're actually adding the opposite. So positive terms become negative, and negative terms become positive.
a² + a - 1
- (3a² - 2a + 5) becomes:
-3a²+2a-5
3. Add the two lines together.
(a²-3a²) + (a+2a) + (-1-5)
This simplifies to:
-2a² + 3a - 6
Therefore, when we subtract 3a² - 2a + 5 from a² + a - 1, we get -2a² + 3a - 6.