# How do you factor #a^4+4b^4# ?

##### 1 Answer

#### Explanation:

This polynomial factors nicely into two quadratic polynomials with integer coefficients:

#a^4+4b^4 = (a^2-2ab+2b^2)(a^2+2ab+2b^2)#

These quadratic factors have no simpler linear factors with Real coefficients. To see that, you can check their discriminants:

#Delta_(a^2-2ab+2b^2) = (-2)^2-4(1)(2) = 4-8 = -4#

#Delta_(a^2+2ab+2b^2) = 2^2-4(1)(2) = 4-8 = -4#

**Footnotes**

Factoring homogeneous polynomials is very similar to factoring a corresponding polynomial in one variable.

In our example, we could let

#t^4+4 = (t^2-2t+2)(t^2+2t+2)#

Then we could multiply this through by

Similarly, when we look at

#t^2-2t+2#

When you have a quadratic of the form

Faced with