(2√2-3√3)(3√3+2√2) = (2√2 3√3) + (2√2 2√2) - (3√3 3√3) - (3√3 * 2√2)= 6√6 + 4√4 - 9 - 6√6= 4 - 9= -5
(6 - √2)^2 + 3√3^2 = (6 - √2)(6 - √2) + 3(3)= 36 - 6√2 - 6√2 + 2 + 9= 47 - 12√2
((√2 - √18)^2) - 30(5√7 - 13)(5√7 + 13) = (2 - 3√2)^2 - 30(25√49 - 169)= 4 - 12√2 + 18 + 7500 - 5070= 7522 - 12√2
(2√2-3√3)(3√3+2√2) = (2√2 3√3) + (2√2 2√2) - (3√3 3√3) - (3√3 * 2√2)
= 6√6 + 4√4 - 9 - 6√6
= 4 - 9
= -5
(6 - √2)^2 + 3√3^2 = (6 - √2)(6 - √2) + 3(3)
= 36 - 6√2 - 6√2 + 2 + 9
= 47 - 12√2
((√2 - √18)^2) - 30(5√7 - 13)(5√7 + 13) = (2 - 3√2)^2 - 30(25√49 - 169)
= 4 - 12√2 + 18 + 7500 - 5070
= 7522 - 12√2