Answer:
To divide (15u^4y^2 + 10u^3y) by (-2u^4y^2), we can simplify the expression by canceling out common factors:
1. Start by factoring out the common factors in the numerator and denominator. In this case, we have:
(15u^4y^2 + 10u^3y) / (-2u^4y^2) = (5u^3y(3u + 2)) / (-u^4y^2)
2. Next, divide each term in the numerator by the denominator. Since we have a negative sign in the denominator, it will affect the overall sign of the expression. Dividing each term gives us:
(5u^3y(3u + 2)) / (-u^4y^2) = -5(3u + 2) / u
3. Simplify the expression further if possible. In this case, there are no more common factors that can be canceled out.
Therefore, the simplified form of (15u^4y^2 + 10u^3y) / (-2u^4y^2) is -5(3u + 2) / u.