2014/073) factor $bca^2 + bcd^2 + adb^2 +adc^2$

this looks non trivial but we can treat is a quadratic in a
bca^2 + a(db^2 + dc^2) + bcd^2

now product of bc and $bcd^2$ is $b^2c^2d^2$ which is product of $db^2$ and $b^2$

so we get $(bca^2 + adb^2) + (adc^2+bcd^2)$
=$ab(ac+bd) + cd(ac + bd)$
= $(ac+bd)(ab+cd)$