Answer:
When we add the given polynomials the result is
[tex](-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)[/tex]
Step-by-step explanation:
Given polynomials are
[tex]-3x^2-2xy+y^2[/tex] ,[tex]-4x^2-xy+6y^2[/tex] , [tex]x^2+6xy-y^2[/tex]
Now addding the polynomials we get
[tex](-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=-3x^2-2xy+y^2+-4x^2-xy+6y^2+x^2+6xy-y^2[/tex]
[tex]=-6x^2+3xy+6y^2[/tex] (adding the like terms on RHS)
[tex]=3(-2x^2+xy+2y^2)[/tex] (taking 3 outside on RHS)
[tex]=3(2(-x^2+y^2)+xy)[/tex]
Rewritting the above equation we get,
[tex]=3(2(y^2-x^2)+xy)[/tex]
Therefore [tex](-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)[/tex]
When we add the given polynomials the result is
[tex](-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)[/tex]
