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express in the form a+b √3

2(3- √3) -3(1- √3)

 Sep 16, 2018
 #1
avatar+2421 
+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
avatar+4586 
+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 \(\boxed{3+\sqrt{3}}.\)

smileysmiley

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 Sep 16, 2018

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