How do you expand and simplify each expression $(-sqrt6 + 2)(2sqrt2 - 3sqrt5 + 1)$ ?

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Answer 1 · 2015-03-24T02:56:50

Start by using the distributive property then see if any roots can be simplified.

$(color(red)(-sqrt(6))+color(green)(2))(2sqrt(2) - 3sqrt(5) + 1)$

$= color(red)((-sqrt(6))(2sqrt(2) - 3sqrt(5) + 1)) color(green)(+(2)(2sqrt(2) - 3sqrt(5) +1)$

$= color(red)(-2sqrt(12) +3sqrt(30) -sqrt(6)) color(green)(+ 4sqrt(2) -6sqrt(5) + 2)$

$= -4sqrt(3) + 3sqrt(30) - sqrt(6) +4sqrt(2) -6sqrt(5) + 2$

How do you expand and simplify each expression (-sqrt6 + 2)(2sqrt2 - 3sqrt5 + 1)(-sqrt6 + 2)(2sqrt2 - 3sqrt5 + 1)?