Question

(ax+by)^2+(ay-bx)^2+c^2x^2+c^2y^2分解因式

Answer 1

(ax+by)^2+(ay-bx)^2+c^2x^2+c^2y^2

=a^2x^2+2abxy+b^2y^2+a^2y^2-2abxy+b^2x^2+c^2x^2+c^2y^2

=x^2(a^2+b^2+c^2)+y^2(a^2+b^2+c^2)

=(a^2+b^2+c^2)(x^2+y^2)