Question

which identity could be used to rewrite the expression x^9-8 A.Two squares B.difference of squares C. difference of cubes D. quadratic formula

Answer 1

We are given expression :
`x^9-8`.

Let us write 8 in factored form.

8 could be factored as 2×2×2.

2×2×2 =
`(2)^3`.

Let us convert
`x^9` also in terms of cube of a term.

`x^9` could be written as the factors of
`x^3 * x^3 * x^3`.

`x^3 * x^3 * x^3 = (x^3)^3`.

Therefore,
`x^9-8= (x^3)^3-2^3`.

Which shows the difference of cubes.

Therefore, correct option is C. difference of cubes.