Problem
ALG-B1-M02-P018 A Fourth Degree Without Expansion
#18
★★★☆☆ Level 3 of 5
Factor \(a^4+a^2b^2+b^4\).
Write the expression as \((a^2+b^2)^2-a^2b^2\).
\(a^4+a^2b^2+b^4=(a^2+b^2)^2-a^2b^2\).
This is a difference of squares: \((a^2-ab+b^2)(a^2+ab+b^2)\).
The hidden step is to create the missing \(a^2b^2\) inside the square.