Samantha thinks that the equation $\left(x − 4\right)^{2} + \left(y − 3\right)^{2} = 25$ is equivalent to the equation $\left(x − 4\right) + \left(y − 3\right) = 5$. Is she correct? Are the two equations equivalent? Explain how you know. If they are not equivalent, explain Samantha's mistake.