Problem
ALG-B1-M02-P006 A Hidden Difference of Squares
#6
★★☆☆☆ Level 2 of 5
Factor \(x^4+4y^4\).
Add and subtract \(4x^2y^2\).
\(x^4+4y^4=x^4+4x^2y^2+4y^4-4x^2y^2=(x^2+2y^2)^2-(2xy)^2\).
Hence \(x^4+4y^4=(x^2-2xy+2y^2)(x^2+2xy+2y^2)\).
One of the central tricks of the module.