1. Simplify: (3y^2-5y^3-4y+1)+(-9y^3+y^2+y-2)

To simplify the given expression, we need to combine like terms. Let's break it down step by step:<br /><br />Given expression:<br />\[<br />(3y^{2} - 5y^{3} - 4y + 1) + (-9y^{3} + y^{2} + y - 2)<br />\]<br /><br />First, distribute the terms inside the parentheses:<br />\[<br />3y^{2} - 5y^{3} - 4y + 1 - 9y^{3} + y^{2} + y - 2<br />\]<br /><br />Next, combine like terms:<br />- For \(y^3\) terms: \(-5y^{3} - 9y^{3} = -14y^{3}\)<br />- For \(y^2\) terms: \(3y^{2} + y^{2} = 4y^{2}\)<br />- For \(y\) terms: \(-4y + y = -3y\)<br />- For constant terms: \(1 - 2 = -1\)<br /><br />So, the simplified expression is:<br />\[<br />-14y^{3} + 4y^{2} - 3y - 1<br />\]<br /><br />Therefore, the correct answer is:<br />\[<br />-14y^{3} + 4y^{2} - 3y - 1<br />\]