Разложите на множители: 2x^2+xy-15y^2

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