What is the numerical coefficient of $x y$ in the following expression?
$x^{5} + 4 x^{2} + 3 x y + y^{2} + 13 x - 7 y x + 7 x^{3} - 2 x y + 5 y$ ?

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-6

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-2

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Solution

The correct option is C -6
The given expression is
$x^{5} + 4 x^{2} + 3 x y + y^{2} + 13 x - 7 y x + 7 x^{3} - 2 x y + 5 y$

Grouping the like terms together and simplifying the expression, we get,
$= x^{5} + 4 x^{2} + (3 x y - 7 y x - 2 x y) + y^{2} + 13 x + 7 x^{3} + 5 y$
$= x^{5} + 7 x^{3} + 4 x^{2} - 6 x y + y^{2} + 13 x + 5 y$

So, the numerical coefficient of xy = - 6

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