How do you factor the expression 2x(x-5)^4-x^2(4)(x-5)^32x(x−5)4−x2(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))2x(x−5)4−x2(4)(x−5)3=−2x(x−5)3(x+5)

Explanation:

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

2x(x-5)^4-x^2(4)(x-5)^32x(x−5)4−x2(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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