Question

Разложи на множители: (y14+x14)²−(y14−x14)²−y2x² .

Answer 1

$(y^{14}+x^{14})^2-(y^{14}-x^{14})^2-y^2x^2=\\=y^{28}+2x^{14}y^{14}+x^{28}-(y^{28}-2x^{14}y^{14}+x^{28})-x^2y^2=\\=4x^{14}y^{14}-x^2y^2=(2x^7y^7)^2-(xy)^2=\\=(2x^7y^7-xy)(2x^7y^7+xy)=xycdot xycdot (2x^6y^6-1)(2x^6y^6+1)=\\=x^2y^2cdot (sqrt2x^3y^3-1)(sqrt2x^3y^3+1)(2x^6y^6+1)=\\=x^2y^2, (sqrt[6]2xy-1)(sqrt[3]2x^2y^2+sqrt[6]2xy+1) (sqrt[6]2xy+1)(sqrt[3]2x^2y^2-sqrt[6]2xy+1)times \\times (sqrt[3]2x^2y^2+1)(sqrt[3]4x^4y^4-sqrt[3]2x^2y^2+1)$