Question

Using complete sentences, explain how you would factor completely x^12 – 8.

Answer 1

We have
\[x^{12}-8\]
we know
\[x^{12}=(x^4)^3\]
and\[8=2^3\]
so we have now the expression as
\[({x^4})^3-2^3\]
we know
\[(a-b)^3=(a-b)(a^2+ab+b^2)\]
using this we get
\[({x^4})^3-2^3=(x^4-2)(x^8+2x^4+4)\]

Answer 2

or
\[x^{12}-8=(x^4-2)(x^8+2x^4+4)\]