Answer to Question #223480 in Algebra for Ata

Question

(2+√y)^2-(2-√y)^2=8√y but in your solution it is equal to 4√y what's the reason.

Answer 1

$(2+\sqrt{y})^2-(2-\sqrt{y})^2\\ =((2+\sqrt{y})+(2-\sqrt{y}))((2+\sqrt{y})-(2-\sqrt{y}))\\ =(2+2+\sqrt{y}-\sqrt{y})(2-2+\sqrt{y}+\sqrt{y})\\ =(4)(2\sqrt{y})\\ =8\sqrt{y}\\ \hspace{0.0cm}\\ \textsf{Hence,}\\ (2+\sqrt{y})^2-(2-\sqrt{y})^2=8\sqrt{y}\not=4\sqrt{y}\\$