How do you factor the expression #2x(x-5)^4-x^2(4)(x-5)^3#?

1 Answer
Alan P.
Jul 26, 2016

#2x(x-5)^4-x^2(4)(x-5)^3=color(green)(-2x(x-5)^3(x+5))#

Explanation:

Since #x^2(4)=(2x)*(2x)

#2x(x-5)^4-x^2(4)(x-5)^3#
#color(white)("XXX")=underline(color(red)(2x) * color(blue)((x-5)^3) * (x-5))-underline(color(red)(2x) * 2x * color(blue)((x-5)^3))#

Extracting the common factors:
#color(white)("XXX")=color(red)(2x) * color(blue)((x-5)^3) * (underline(""(x-5))-underline(2x))#

#color(white)("XXX")=color(red)(2x) * color(blue)(""(x-5)^3) * (-1)(x+5)#

#color(white)("XXX")=-2x(x-5)^3(x+5)#

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