Question

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

Answer 1

`(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`