How do you simplify #(x^3 - 1)/(x-1)#?

1 Answer
Apr 5, 2016

Answer:

#(x^3-1)/(x-1) = x^2+x+1#

Explanation:

In general
#color(white)("XXX")(x^3-a^3)# can be factored as: #(x-1)(x^2+ax+a^2)#
Replacing #a=1# gives the result in the "Answer"

#underline(" X | " x^2 color(white)("XX") +axcolor(white)("XXXXX") +a^2)#
#x color(white)("X")" | "color(white)("XX") x^3 color(white)("XX") +cancel(ax^2) color(white)("XX") +cancel(a^2x)#
#-a" | " cancel(-ax^2) color(white)("XX") cancel(a^2x)color(white)("XXXX") -a^2#