\(a^4+b^4\\ =\left(a^4+2a^2b^2+b^4\right)-2a^2b^2\\ =\left(a^2+b^2\right)^2-2a^2b^2\\ =\left[\left(a^2+2ab+b^2\right)-2ab\right]^2-2a^2b^2\\ =\left[\left(a+b\right)^2-2ab\right]^2-2a^2b^2\\ =\left(a+b\right)^4-4ab\left(a+b\right)^2+4a^2b^2-2a^2b^2\\ =\left(-4\right)^4-4\left(-12\right)\left(-4\right)^2+2a^2b^2\\ =256+768+2\left(-12\right)^2\\ =256+768+288\\ =1312\)