If x + y = 24 and x² + y² = 360, then find the value of (x⁴ + x²y² + y⁴).

xy = [(x+y)² − (x²+y²)]/2 = [576−360]/2 = 108. x²+y² = 360, so (x²+y²)² = 129600. x⁴+y⁴ = 129600 − 2(xy)² = 129600 − 23328 = 106272. x⁴+x²y²+y⁴ = 106272 + 11664 = 117936.