#(color(red)(3sqrt11color(green)(+3sqrt15)))(color(blue)(3sqrt3)color(brown)(-2sqrt2))#
Multiply each term in the bracket with each other term in the other bracket
#color(red)(3sqrt11)(color(blue)(3sqrt3))+color(red)(3sqrt11)(color(brown)(-2sqrt2))+color(green)(3sqrt15)(color(blue)(3sqrt3))+color(green)(3sqrt15)(color(brown)(-2sqrt2))#
Multiply the whole number with the whole number and the square root with the square root
#color(red)3*color(blue)3sqrt(color(red)11*color(blue)3)+color(red)3*color(brown)(-2)sqrt(color(red)11*color(brown)2)+color(green)3*color(blue)3sqrt(color(green)15*color(blue)3)+color(green)3*color(brown)(-2)sqrt(color(green)15*color(brown)2)#
#9sqrt33-6sqrt22+9sqrt45-6sqrt30#
#9sqrt45# can be simplified
#9sqrt45=9*sqrt(3*3*5)=9*sqrt(3^2*5)=9*sqrt(3^2)*sqrt5=9*3sqrt5=27sqrt5#
So #9sqrt33-6sqrt22+color(magenta)(9sqrt45)-6sqrt30# can be rewritten as
#9sqrt33-6sqrt22+color(magenta)(27sqrt5)-6sqrt30#
These numbers can't be combined due to different numbers inside the roots, so this is the final answer.
