Question

(√2+1)^2
(√3+ √2)^2
(2-x)^2
(x-3)^2
(√2-√3)^2
(1-√5)^2

Answer 1

$( \sqrt{2} + 1) {}^{2} = 2 + 2 \sqrt{2} + 1 = 3 + 2 \sqrt{6} \: \: \: \: \\ ( \sqrt{3} + \sqrt{2} ) {}^{2} = 3 + 2 \sqrt{6} + 2 = 5 + 2 \sqrt{6} \\ (2 - x) {}^{2} = 4 - 4x + x {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ (x - 3) {}^{2} = x {}^{2} - 6x + 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ( \sqrt{2} - \sqrt{3} ) {}^{2} = 2 - 2 \sqrt{6} + 3 = 5 - 2 \sqrt{6} \\ (1 - \sqrt{5} ) {}^{2} = 1 - 2 \sqrt{5} + 5 = 6 - 2 \sqrt{5} \: \: \: \: \\ \\ \boxed{\large\tt{{(a + b) {}^{2} = a {}^{2} + 2ab + b {}^{2} }}} \\ \\ \boxed{\large\tt{{(a - b) {}^{2} = a {}^{2} - 2ab + b {}^{2} }}}$