Question

proove it not in numbers in letters

Answer 1

As u know the formula of
( a + b )^2 = a^2 + b^2 + 2ab
now, taking 2ab on the left side of the equation.
( a + b )^2 - 2ab = a ^2 + b^2
Hence proved.

Answer 2

consider a as x and b as y just for comfort
${x}^{2} + {y}^{2} = (x + y) {}^{2} - 2xy \\ {x}^{2} + {y}^{2} = {x}^{2} + {y}^{2} + 2xy - 2xy$
since
$(x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy$
so continue to the point
${x}^{2} + {y}^{2} = {x}^{2} + {y}^{2} + 2xy - 2xy \\ = = {x}^{2} + {y}^{2} = {x}^{2} + {y}^{2}$
since
$2xy - 2xy = 0$
hope it helps