#### Answer

$(x+y)^{2} \ne x^{2} + y^{2}$ as this is untrue and can be proven by substitution of numbers into the equation.

#### Work Step by Step

To prove that $(x+y)^{2} \ne x^{2} + y^{2}$
We take numbers, for example, x=5 and y=6 and substitute them into the equation
$(x+y)^{2} = x^{2} + y^{2}$
$(5+6)^{2} = 5^{2} + 6^{2}$
$(11)^{2}$ = 25 + 36
121 $\ne$ 61
Therefore we can prove that $(x+y)^{2} \ne x^{2} + y^{2}$