How do you factor #x^2-y^2-8x+16# ?

1 Answer
George C.
Feb 7, 2017

#x^2-y^2-8x+16 = (x-y-4)(x+y-4)#

Explanation:

The difference of squares identity can be written:

#a^2-b^2=(a-b)(a+b)#

We can use this with #a=(x-4)# and #b=y# as follows:

#x^2-y^2-8x+16 = (x^2-8x+16)-y^2#

#color(white)(x^2-y^2-8x+16) = (x-4)^2-y^2#

#color(white)(x^2-y^2-8x+16) = ((x-4)-y)((x-4)+y)#

#color(white)(x^2-y^2-8x+16) = (x-y-4)(x+y-4)#

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