How do you factor #x^3+15x^2+75x+125#?

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Answer 1 · 2015-05-27T23:11:12

#color(red)(x^3+125 = x^3+5^3 = (x+5)(x^2-5x+25))#

#color(blue)(15x^2+75x = (x+5)(15x))#

#color(red)(x^3) + color(blue)(15x^2)+color(blue)(75x)+color(red)(125)#

Therefore:
#=color(red)((x^3+125)) + color(blue)((15x^2+75))#

#= (x+5)color(red)((x^2-5x+25)) + (x+5)color(blue)((15x))#

#= (x+5)(color(red)(x^2-5x+25)+color(blue)(15x))#

#=(x+5)(x^2+10x+25)#

#=(x+5)^3#