How to Factorize #256-x^2-2xy-y^2#?

1 Answer
George C.
Sep 23, 2017

#256-x^2-2xy-y^2 = (16-x-y)(16+x+y)#

Explanation:

The difference of squares identity can be written:

#A^2-B^2 = (A-B)(A+B)#

Use this with #A=16# and #B=(x+y)# as follows:

#256-x^2-2xy-y^2 = 16^2-(x^2+2xy+y^2)#

#color(white)(256-x^2-2xy-y^2) = 16^2-(x+y)^2#

#color(white)(256-x^2-2xy-y^2) = (16-(x+y))(16+(x+y))#

#color(white)(256-x^2-2xy-y^2) = (16-x-y)(16+x+y)#

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