Question

Add the following polynomails -3x^2-2xy+y^2,-4x^2-xy+6y^2, x^2+6xy-y^2

Answer 1

When we add the given polynomials the result is

`(-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)`

Explanation:

Given polynomials are

`-3x^2-2xy+y^2` ,
`-4x^2-xy+6y^2` ,
`x^2+6xy-y^2`

Now addding the polynomials we get

`(-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`

`=-6x^2+3xy+6y^2` (adding the like terms on RHS)

`=3(-2x^2+xy+2y^2)` (taking 3 outside on RHS)

`=3(2(-x^2+y^2)+xy)`

Rewritting the above equation we get,

`=3(2(y^2-x^2)+xy)`

Therefore
`(-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)`

When we add the given polynomials the result is

`(-3x^2-2xy+y^2)+(-4x^2-xy+6y^2)+(x^2+6xy-y^2)=3(2(y^2-x^2)+xy)`