- Thread starter
- #1
paulmdrdo
Active member
- May 13, 2013
- 386
how to force factor this into the difference of two squares.
$\displaystyle x^4 + 1$
$\displaystyle x^4 + 1$
The idea is complete the square , since if we have for example :I would get this
$\displaystyle \displaystyle \begin{align*} x^4 + 1 &= x^4 + 2x^2 + 1 - 2x^2 \\& = \left( x^2 + 1 \right) ^2 - \left( \sqrt{2} \, x \right) ^2 \\& = \left( x^2 - \sqrt{2}\, x + 1 \right) \left( x^2 + \sqrt{2}\,x + 1 \right) \end{align*}$
but i want to know what's your reasoning by choosing the term 2x^2?