Разложите на множители: 2x^2+xy-15y^2

[latex]2x^2+xy-15y^2=\\=(\sqrt{2}x)^2+2\cdot\sqrt{2}x\cdot\frac{y}{2\sqrt{2}}+(\frac{y}{2\sqrt{2}})^2-(\frac{y}{2\sqrt{2}})^2-15y^2=\\=(\sqrt{2}x+\frac{1}{2\sqrt{2}}y)^2-\frac{1}{8}y^2-15y^2=(\sqrt{2}x+\frac{1}{2\sqrt{2}}y)^2-\frac{121}{8}y^2=\\=(\sqrt{2}x+\frac{1}{2\sqrt{2}}y-\frac{11}{2\sqrt{2}}y)(\sqrt{2}x+\frac{1}{2\sqrt{2}}y+\frac{11}{2\sqrt{2}}y)=\\=(\sqrt{2}x-\frac{10}{2\sqrt{2}}y)(\sqrt{2}x+\frac{12}{2\sqrt{2}}y)=(\sqrt{2}x-\frac{5\sqrt{2}}{2}y)(\sqrt{2}x+3\sqrt{2}y)=\\=2(x-\frac{5}{2}y)(x+3y)[/latex]