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I'm studying basic algebra and I'm a bit confuse about degree of equations. I read quadratic equation are equations of the second degree, meaning it contains at least one term that is squared. My question is if that squared term also can be something like $2xy$ (because the degree of the term is also $2$ (the sum of exponents of each variable): example $2xy + x = 12$ or can only be single variables with exponent $x^2, y^2, \dotsc$.

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    $\begingroup$ Yes, if you have a 2-variable expression, xy is a quadratic term. The degrees of x and y are added, together they give 2. $\endgroup$ – user376343 Jun 4 '20 at 19:51
  • $\begingroup$ A quadratic equation typically considers only one variable. If you have more than one variable it would be a root of a multivariable quadratic function. $\endgroup$ – Peter Foreman Jun 4 '20 at 19:52
  • $\begingroup$ Is "quadratic" the common name in the case $xy$ ? Isn't it just a term with degree $2$ ? $\endgroup$ – Peter Jun 4 '20 at 19:52
  • $\begingroup$ It's not unheard of. For instance $xy$ and $x^2-y^2$ are the same function up to a change of basis, and calling $x^2-y^2$ quadratic would be more common. $\endgroup$ – runway44 Jun 4 '20 at 21:53
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As said in the comments, when dealing with more than one variable you simply add the exponents of each.

For example, the degree of $xy$ is $1+1=2$ (since $x$ and $y$ are raised to the $1$st power.) Similarly, the degree of $x^2y$ is $2+1=3$, and the degree of $xyz$ is $1+1+1=3$.

-FruDe

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