Question 130155
Throughout this problem, keep in mind that {{{z>=0}}} (remember you cannot take the square root of a negative number)


{{{(sqrt( 13) + sqrt( z)) (sqrt( 13) - sqrt( z)) }}} Start with the given expression



{{{sqrt( 13)*sqrt( 13)-sqrt( 13)*sqrt( z)+sqrt(z)*sqrt(13)-sqrt( z)sqrt( z)}}} Foil the expression



{{{sqrt( 13^2)-sqrt( 13z)+sqrt(13z)-sqrt( z^2)}}} Combine the roots



{{{sqrt( 13^2)+cross(-sqrt( 13z)+sqrt(13z))-sqrt( z^2)}}} Cancel like terms



{{{sqrt( 13^2)-sqrt( z^2)}}} Simplify



{{{13-z}}} Take the square root of {{{13^2}}} to get 13. Take the square root of {{{z^2}}} to get z. 



So {{{(sqrt( 13) + sqrt( z)) (sqrt( 13) - sqrt( z)) }}} simplifies to {{{13-z}}}



In other words, {{{(sqrt( 13) + sqrt( z)) (sqrt( 13) - sqrt( z)) =13-z}}}