Final answer:
To obtain an expression with the same value as (6x^2 + 3x - 4) - (3x^2 - 5x + 1), we subtract the second polynomial from the first to get 3x^2 + 8x - 5.
Step-by-step explanation:
To find the expression with the same value as (6x^2 + 3x - 4) - (3x^2 - 5x + 1), we need to subtract the second polynomial from the first. This involves changing the sign of each term in the second polynomial and then combining like terms with the first.
First, change the signs of the second polynomial:
-(3x^2 - 5x + 1) becomes -3x^2 + 5x - 1.
Next, combine like terms with the first polynomial:
(6x^2 + 3x - 4) + (-3x^2 + 5x - 1).
Combine like terms:
6x^2 - 3x^2 + 3x + 5x - 4 - 1.
This simplifies to:
3x^2 + 8x - 5.
So, the expression that has the same value is 3x^2 + 8x - 5.