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

Answer 1

Answer:

Add $-x^2+2xy$

Step-by-step 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.

Answer 2

Answer:

-x^2+2xy

Step-by-step 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