Question

Expand and simplify:3%29" id="TexFormula1" title="( \sqrt{3} + 1)( \sqrt{3} - 3)" alt="( \sqrt{3} + 1)( \sqrt{3} - 3)" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$-2\sqrt{3}$

Step-by-step explanation:

$\textsf{Given expression}: \quad(\sqrt{3}+1)(\sqrt{3}-3)$

$\textsf{Use the FOIL method to expand}\quad(a+b)(c-d)=ac-ad+bc-bd:$

$=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}+1(-3)$

$=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}-3$

$\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{a}=a:$

$=3-3\sqrt{3}+\sqrt{3}-3$

$\textsf{Collect like terms}:$

$=3-3-3\sqrt{3}+\sqrt{3}$

$\textsf{Combine like terms}:$

$=0-2\sqrt{3}$

$=-2\sqrt{3}$