r) (a^2-0,5a-1)-(1,5a^2+a+2)+(0,5a^2+3)

To simplify the given expression, we need to combine like terms. Let's break it down step by step:<br /><br />Given expression:<br />\[<br />(a^{2} - 0.5a - 1) - (1.5a^{2} + a + 2) + (0.5a^{2} + 3)<br />\]<br /><br />First, distribute the negative sign in the second term:<br />\[<br />(a^{2} - 0.5a - 1) - 1.5a^{2} - a - 2 + 0.5a^{2} + 3<br />\]<br /><br />Next, combine like terms:<br />\[<br />a^{2} - 0.5a - 1 - 1.5a^{2} - a - 2 + 0.5a^{2} + 3<br />\]<br /><br />Combine the \(a^2\) terms:<br />\[<br />a^{2} - 1.5a^{2} + 0.5a^{2} = (1 - 1.5 + 0.5)a^{2} = 0a^{2} = 0<br />\]<br /><br />Combine the \(a\) terms:<br />\[<br />-0.5a - a = -1.5a<br />\]<br /><br />Combine the constant terms:<br />\[<br />-1 - 2 + 3 = 0<br />\]<br /><br />Putting it all together, we get:<br />\[<br />0 - 1.5a + 0 = -1.5a<br />\]<br /><br />So, the simplified expression is:<br />\[<br />-1.5a<br />\]