Problem
ALG-B1-M01-P014 Two-Level Substitution
#14
★★★☆☆ Level 3 of 5
Factor \(x^4+2x^2y^2+y^4-16\).
First recognise the square \((x^2+y^2)^2\).
We have \(x^4+2x^2y^2+y^4=(x^2+y^2)^2\). Thus the expression is \((x^2+y^2)^2-4^2\).
By difference of squares, it factors as \((x^2+y^2-4)(x^2+y^2+4)\). Over the reals, the second factor does not split further.
Good illustration of block substitution.