Question

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

Answer 1

`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)`