Suppose that the equation \[x^4 + Ax^2 + B = (x^2 + ax + b)(x^2 - ax + b)\] holds for all values of \(x\).
Find \(A\) and \(B\) in terms of \(a\) and \(b\).
Use this information to find a factorisation of the expression \[x^4 - 20x^2 + 16\] as a product of two quadratics in \(x\).
Show that the four solutions of the equation \[x^4 - 20x^2 + 16 = 0\] can be written as \(\pm \sqrt{7} \pm \sqrt{3}\).
