factoring polynomial equations

Oct 2012
1
0
us
81x^4-256

im working on a problem and need to factor the above equation. thanks for your help in advance.
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
\(\displaystyle \displaystyle \begin{align*} 81x^4 - 256 &= \left( 9x^2 \right)^2 - 16^2 \\ &= \left( 9x^2 - 16 \right) \left( 9x^2 + 16 \right) \\ &= \left[ \left(3x \right)^2 - 4^2 \right] \left( 9x^2 + 16 \right) \\ &= \left( 3x - 4 \right) \left( 3x + 4 \right) \left( 9x^2 + 16 \right) \end{align*}\)