# Classify the following quadric surface

#### scolon94

##### New member
x2-2xy +2y2-2yz+z2=0
hint: 2y2=y2+y2
I thought of replacing 2y^2. But I'm not sure exactly what to do.
Thank you.

#### MarkFL

Staff member
Use the given hint allow with the property of associativity to write:

$$\displaystyle \left(x^2-2xy+y^2 \right)+\left(y^2-2yx+z^2 \right)=0$$

Now do you see how to proceed?

#### scolon94

##### New member
Use the given hint allow with the property of associativity to write:

$$\displaystyle \left(x^2-2xy+y^2 \right)+\left(y^2-2yx+z^2 \right)=0$$

Now do you see how to proceed?
I'm still confused because of the -2xy and -2yz. Is it possible to complete the square?

#### MarkFL

What is the expansion of $(a-b)^2$?
Also $$a^2+ b^2= 0$$ if and only if a= b= 0.