Multivariable Polynomials: Intro and Various "Degrees"

A multivariable polynomial is a polynomial with multiple variables within it. For example: $$a^4b^2+7a^3b^5+6$$ is a $2$-variable polynomial. The degree of these multivariable polynomials is the highest total power (add up the powers for all variables). Our previous example's degree would be $8$ because the sum of the powers for the first, second, and third term is $4+2=6$, $3+5=8$, and $0$ respectively, and the highest power if $8$, so $8$ is our degree.