The sum of $x^{4} - x y + 2 y^{2}$ and $- x^{4} + x y + 2 y^{2}$ is

monomial

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binomial

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trinomial

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None of the above

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Solution

The correct option is A monomial
Required sum $= (x^{4} - x y + 2 y^{2}) + (- x^{4} + x y + 2 y^{2})$
$= x^{4} - x y + 2 y^{2} - x^{4} + x y + 2 y^{2} = [(x^{4} + (- x^{4}))] + (- x y + x y) + (2 y^{2} + 2 y^{2}) = 0 + 0 + 4 y^{2} = 4 y^{2}$
$4 y^{2}$ is a monomial and polynomial in y.
Hence option (a) is correct.

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Out of the four options, only one is correct. Write the correct answer.

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(b) binomial and polynomial
(c) trinomial and polynomial
(d) monomial and polynomial in x

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