Question

Find the value of $2(\sqrt{3}{)}^6+18-4(\sqrt{3}{)}^3$ ?

• A. $3\sqrt{3}(4\sqrt{3}+2)$
• B. $6\sqrt{3}(2\sqrt{3}-2)$
• C. $6\sqrt{3}(4\sqrt{3}-2)$
• D. $6\sqrt{3}(4\sqrt{3}+2\sqrt{3})$

Answer 1

The correct option is C $6\sqrt{3}(4\sqrt{3}-2)$

$2(\sqrt{3}{)}^6+18-4(\sqrt{3}{)}^3$
= $2(\sqrt{3}{)}^6+2\times 9-4(\sqrt{3}{)}^3$
= $2(\sqrt{3}{)}^6+2(\sqrt{3}{)}^4-4(\sqrt{3}{)}^3$
Now, taking $(2\sqrt{3}{)}^3$ common from the expression
$2\left(\sqrt{3}{)}^3\right((\sqrt{3}{)}^3+\sqrt{3}-2)$
= $6\sqrt{3}\left(3\sqrt{3}\right)+\sqrt{3}-2)$
=$6\sqrt{3}(4\sqrt{3}-2)$