Answer:
[tex]-2\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\textsf{Given expression}: \quad(\sqrt{3}+1)(\sqrt{3}-3)[/tex]
[tex]\textsf{Use the FOIL method to expand}\quad(a+b)(c-d)=ac-ad+bc-bd:[/tex]
[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}+1(-3)[/tex]
[tex]=\sqrt{3}\sqrt{3}-3\sqrt{3}+1\sqrt{3}-3[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{a}=a:[/tex]
[tex]=3-3\sqrt{3}+\sqrt{3}-3[/tex]
[tex]\textsf{Collect like terms}:[/tex]
[tex]=3-3-3\sqrt{3}+\sqrt{3}[/tex]
[tex]\textsf{Combine like terms}:[/tex]
[tex]=0-2\sqrt{3}[/tex]
[tex]=-2\sqrt{3}[/tex]
