help pleaseee

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express in the form a+b √3

2(3- √3) -3(1- √3)

Guest Sep 16, 2018

TheXSquaredFactor · Answer 1 · 2018-09-16T08:03:03

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, $a+b\sqrt{3}$

tertre · Answer 2 · 2018-09-16T08:04:44

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 $\boxed{3+\sqrt{3}}.$