Answer: A) –6x⁴y – 2x³y² + 9x²y³ – 3xy⁴ + y⁵
Explanation:
To simplify this, we combine like terms. Like terms are those with the same variables and exponents.
Our original expression is
(-2x³y²+4x²y³-3xy⁴)-(6x⁴y-5x²y³-y⁵)
The first term, -2x³y², does not have any like terms; there no other terms with x and an exponent of 3 and y and an exponent of 2.
The second term, 4x²y³, has a like term, -5x²y³. They have the same variables and exponents. These are to be subtracted:
4x²y³--5x²y³ = 4x²y³+5x²y³ = 9x²y³
The third term, -3xy⁴, has no like terms.
The fourth term, 6x⁴y, has no like terms; but since it is in the expression being subtracted, it is negative.
We have already combined like terms with the fifth term.
The sixth term, -y⁵, has no like terms; but since it is in the expression being subtracted, it is a double negative, which makes it a positve.
This gives us
-2x³y²+9x²y³-3xy⁴-6x⁴y+y⁵
Rewriting this in order by exponent of x, we have
-6x⁴y-2x³y²+9x²y-3xy⁴+y⁵