Question

What binomial do you have to add to the polynomial x^2+y^2–2xy+1 to get a polynomial: not containing the variable x

Pls Help me!

Answer 1

-x^2+2xy

Explanation:

x^2 + y^2 -2xy + 1 +something = y^2 +1

This will get rid of the x and x^2 terms

Subtract y^2 from each side

x^2 + y^2 -y^2 -2xy + 1 +something = y^2-y^2 +1

x^2 -2xy+1 +something = 1

Subtract 1 from each side

x^2 -2xy+1 -1+something = 1-1

x^2 -2xy+something = 0

Subtract x^2 from each side

x^2 -x^2 -2xy+something = 0-x^2

-2xy+something = -x^2

Add 2xy to each side

2xy -2xy+something = -x^2+2xy

something = -x^2+2xy

We need to add -x^2+2xy

Remember a binomial is 2 terms

Answer 2

Add
`-x^2+2xy`

Explanation:

The polynomial
`x^2+y^2-2xy+1` can be added to eliminate the x terms by adding the additive inverse. We add
`-x^2+2xy` which has the inverse sign value of the polynomial terms.

`(x^2+y^2-2xy+1)+(-x^2+2xy)`

`x^2-x^2+y^2-2xy+2xy+1`

When we simplify, this leaves
`y^2+1` without an x term.