+2446 All that is necessary is some simplifying. That's all.
| \(2(3-\sqrt{3})-3(1-\sqrt{3})=a+b\sqrt{3}\) | Let's simplify the left-hand side as much as possible and see if there is any parallelism. The first step is to distribute. |
| \(6-2\sqrt{3}-3+3\sqrt{3}=a+b\sqrt{3}\) | Now, combine like terms together. |
| \(\)\(\textcolor{red}{3}+\textcolor{blue}{1}\sqrt{3}=\textcolor{red}{a}+\textcolor{blue}{b}\sqrt{3}\) | I have used colors to highlight the parallelism between the left-hand side and the right-hand side. This means that I have written the original expression in the desired form, \(a+b\sqrt{3}\) |
+4622
First, expand \(2(3- \sqrt3)\) to \(6-2\sqrt3\) , by applying the distributive property, ab-ac.
Next, we expand the second term, \(-3(1- \sqrt3)\) to \(-3+3\sqrt{3}\) , by again using the distributive property.
Finally, we simplify, (by adding similar elements), \(6-2\sqrt{3}-3+3\sqrt{3}\) and that will get us \(\boxed{3+\sqrt{3}}.\)
