<s>[INST] Question on Factoring I have very basic Question about factoring, we know that,
$$x^2+2xy+y^2 = (x+y)^2$$
$$x^2-2xy+y^2 = (x-y)^2$$
But what will 
$$x^2-2xy-y^2 = ??$$
$$x^2+2xy-y^2 = ??$$
 [/INST] This is another way of solving this problem using Completing the Square method.
$x^2+2xy-y^2=??$
First we have,
$x^2+2xy-y^2=0$
$x^2+2xy=y^2,$
By adding both sides by $y^2$ to make it perfect square then,
$x^2+2xy+y^2=y^2+y^2$
$(x+y)^2=2y^2$
$x+y=[2^(1/2)]y$
$x=(+ or -)[2^(1/2)]y-y$
$x=[2^(1/2)]y-y  ; x=-[2^(1/2)]y-y $
$x=[2^(1/2)-1]y   ; x=-[2^(1/2)-1]y$
therefore we have,
${x-[2^(1/2)-1]y}{x+[2^(1/2)-1]y}$
By solving 
$x^2-2xy-y^2=??$
Try to solve this by relying with this pattern. Thank you.
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