Following algebraic expression is polynomial or not? If so, write the degree.
$x^{2} - 4 x^{2} y + 3 x y$

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Solution

Given algebraic expression $x^{2} - 4 x^{2} y + 3 x y$
It is an algebraic expression of variables $x$ and $y$
An algebraic expression is said to be a polynomial if the power of the variable is non-negative.
The power of the variable is positive in given algebraic expression $x^{2} - 4 x^{2} y + 3 x y$
Thus, it is a polynomial.
Since,
Degree of term $x^{2} = 2$
Degree of term $- 4 x^{2} y = 2 + 1 = 3$
Degree of term $3 x y = 1 + 1 = 2$
Therefore,
Maximum degree $= 3$
Thus, the degree of the polynomial $x^{2} - 4 x^{2} y + 3 x y$ is $3$
Hence, the given algebraic expression is a polynomial of degree three.

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