Question 358123
{{{( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) )}}}
This expression is similar to
(2x - 3y)(3x + 6y)
and we do the same thing to multiply: Use FOIL (or whatever technique you have learned to multiply polynomials):
{{{2sqrt(3)*3sqrt(3) + 2sqrt(3)*6sqrt(6) -4sqrt(6)3sqrt(3) -4sqrt(6)6sqrt(6)}}}
Within each product we will multiply the coefficients and use the property of radicals, {{{root(a, p)*root(a, q) = root(a, p*q)}}}, to multiply the square roots:
{{{6sqrt(3*3) + 12sqrt(3*6) -12sqrt(6*3) -24sqrt(6*6)}}}
which simplifies as follows:
{{{6sqrt(9) + 12sqrt(18) -12sqrt(18) -24sqrt(36)}}}
Since {{{sqrt(9) = 3}}} and {{{sqrt(36) = 6}}} and since the two middle terms cancel out:
{{{6*3 -24*6}}}
{{{18 - 144}}}
{{{-126}}}
So
{{{( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) ) = -126}}}