Question

Expand and simplify:


`( √(3) + 1)( √(3) - 3)`
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Answer 1

`-2√(3)`

Explanation:

`\textsf{Given expression}: \quad(√(3)+1)(√(3)-3)`

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

`=√(3)√(3)-3√(3)+1√(3)+1(-3)`

`=√(3)√(3)-3√(3)+1√(3)-3`

`\textsf{Apply radical rule} \quad √(a)√(a)=a:`

`=3-3√(3)+√(3)-3`

`\textsf{Collect like terms}:`

`=3-3-3√(3)+√(3)`

`\textsf{Combine like terms}:`

`=0-2√(3)`

`=-2√(3)`