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express in the form a+b √3

2(3- √3) -3(1- √3)

Sep 16, 2018

#1
+1

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, $$a+b\sqrt{3}$$
Sep 16, 2018
#2
+1

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 $$\boxed{3+\sqrt{3}}.$$  .
Sep 16, 2018