Final answer:
To simplify the expression, combine like terms and perform any operations within the expression. The result is 4k^2 - 5k + 3v^2, which is the fully simplified form.
Step-by-step explanation:
To fully simplify the expression 3k^2-7k+5v^2+(-k)^2+2k-2v^2, we need to combine like terms and simplify any operations within the expression.
- First, we simplify (-k)^2 to k^2 since the square of a negative number is positive.
- Next, we combine the like terms: 3k^2 and k^2 become 4k^2; -7k and 2k become -5k; 5v^2 and -2v^2 become 3v^2.
- Now the expression looks like this: 4k^2 - 5k + 3v^2.
This is the fully simplified form of the expression, as there are no more like terms to combine.