Question 179563
{{{(a+b)^2= a^2+b^2}}} is NOT true in general, here's why:



{{{(a+b)^2= a^2+b^2}}} Start with the given equation.



{{{a^2+2ab+b^2= a^2+b^2}}} FOIL



{{{cross(a^2-a^2)+2ab+cross(b^2-b^2)= cross(a^2-a^2)+cross(b^2-b^2)}}} Subtract {{{a^2}}} from both sides. Subtract {{{b^2}}} from both sides. Notice how the {{{a^2}}} and the {{{b^2}}} terms cancel out.



{{{2ab=0}}} Simplify



{{{a=0}}} or {{{b=0}}} Set each individual factor equal to zero



So {{{(a+b)^2= a^2+b^2}}} is only true if {{{a=0}}} or {{{b=0}}} (or both are zero). However, for <i>any</i> other values of "a" and "b", {{{(a+b)^2= a^2+b^2}}} is NOT true.




Here's an example to support the answer:



{{{(a+b)^2= a^2+b^2}}} Start with the given equation.



{{{(2+3)^2=2^2+3^2}}} Plug in {{{a=2}}} and {{{b=3}}} (just pick 2 random values. Make sure that both are nonzero values)



{{{5^2=2^2+3^2}}} Add



{{{5^2=4+3^2}}} Square 2 to get 4



{{{5^2=4+9}}} Square 3 to get 9



{{{25=4+9}}} Square 5 to get 25



{{{25=13}}} Add



Since {{{25<>13}}}, this means that we've just shown an example where {{{(a+b)^2= a^2+b^2}}} is not true. So {{{(a+b)^2= a^2+b^2}}} is not true in general