Question

why is
$( \alpha - \beta ) ^{2} = ( \alpha + \beta ) ^{2} - 4 \alpha \beta$
​

Answer 1

( a - b)^2 = ( a + b )^2 - 4ab

a^2 + b^2 - 2ab = a^2 + b^2 + 2ab - 4ab

a^2 + b^2 - 2ab = a^2 + b^2 - 2ab

hence proved