Question

What is the remainder when x^4-y^4 is divided by x-y?

Answer 1

$x^{4} - {y}^{4} \\ \\ {x}^{4} - {x}^{3} y + {x}^{3} y - {x}^{2} {y}^{2} + {x}^{2} {y}^{2} - x {y}^{3} + x {y}^{3} - {y}^{4} \\ \\ {x}^{3} (x - y) + {x}^{2}y (x - y) + x {y}^{2} (x - y) + {y}^{3} (x - y) \\ \\ (x - y)( {x}^{3} + {x}^{2} y + x {y}^{2} + {y}^{3} )$

So the remainder is 0.