Factorization of a⁴ + b⁴ − a²b²
The factorized form of \[ a^4+b^4-a^2b^2 \] is __________
Solution
\[ a^4+b^4-a^2b^2 \]
\[ =(a^2+b^2)^2-3a^2b^2 \]
\[ =(a^2+b^2)^2-(\sqrt{3}ab)^2 \]
\[ =(a^2+b^2-\sqrt{3}ab)(a^2+b^2+\sqrt{3}ab) \]
\[ \boxed{(a^2+b^2-\sqrt{3}ab)(a^2+b^2+\sqrt{3}ab)} \]