Question

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

Answer 1

Answer:

When we add the given polynomials the result is

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

Step-by-step 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

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