Using the binary operation defined as (a,b) = a\^2 + b\^2, how can we transform the expression a\^2 + b\^2 + c\^2 such that only this operation that i defined and no other mathematical operations(+,-,\*,/,exp.,etc) except for the square root (√) are present in the final expression? Please provide a step-by-step deductive reasoning process to arrive at the answer.