Question 614658
{{{(sqrt(6)-6)(sqrt(3)+4)}}}
First of all, this is not an equation. There is no equals sign. It is an expression. And expressions are simplified, not solved.<br>
Just as with any pair of binomials (two-term expressions), you use FOIL to multiply:
F: {{{sqrt(6)*sqrt(3)}}}
Using the property of radicals, {{{root(a, p)*root(a, q) = root(a, p*q)}}}, this becomes:
{{{sqrt(6*3) = sqrt(18)}}}
And since 18 has a perfect square factor, {{{sqrt(18)}}} will simplify:
{{{sqrt(18) = sqrt(9*2) = sqrt(9)*sqrt(2) = 3sqrt(2)}}}<br>
O: {{{sqrt(6)*4 = 4sqrt(6)}}}
I: {{{-6*sqrt(3) = -6sqrt(3)}}}
L: {{{-6*4 = -12}}}<br>
Putting this all together we get:
{{{(sqrt(6)-6)(sqrt(3)+4) = 3sqrt(2) + 4sqrt(6) + (-6sqrt(3)) + (-12)}}}
None of these terms are like terms so they cannot be added. This expression (or, if you prefer subtractions, {{{3sqrt(2) + 4sqrt(6) -6sqrt(3) -12}}}) is the simplified expression.