Question

Sabendo que x.y=k+z determine o monômio z e sendo x=2x²y³ y=-4xy e k=-14x³y^4
entao z é igual a ?

Answer 1

$x=2x^{2}y^{3}\\ \\ y=-4xy\\ \\ k=-14x^{3}y^{4}\\ \\ xy=k+z \Rightarrow z=xy-k\\ \\ \\ z=\left(2x^{2}y^{3} \right )\left(-4xy \right)-\left(-14x^{3}y^{4} \right )\\ \\ z=-8x^{2+1}y^{3+1}+14x^{3}y^{4}\\ \\ z=-8x^{3}y^{4}+14x^{3}y^{4}\\ \\ z=\left(-8+14 \right )x^{3}y^{4}\\ \\ \boxed{z=6x^{3}y^{4}}$