Write in simple form:
$(14 x^{1000} + 20 x^{10} y^{5} + 3 y^{1000}) + (- 2 y^{1000} - 10 x^{10} y^{5} + x^{2} - 14 x^{1000})$

30 x^{10} y^{5} + 5 y^{1000} + x^{2}

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10 x^{10} y^{5} + y^{1000} + x^{2}

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10 x^{10} y^{5} + 5 y^{1000} + x^{2}

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30 x^{10} y^{5} + y^{1000} + x^{2}

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Solution

The correct option is B $10 x^{10} y^{5} + y^{1000} + x^{2}$
$(14 x^{1000} + 20 x^{10} y^{5} + 3 y^{1000}) + (- 2 y^{1000} - 10 x^{10} y^{5} + x^{2} - 14 x^{1000})$

$= 14 x^{1000} + 20 x^{10} y^{5} + 3 y^{1000} - 2 y^{1000} - 10 x^{10} y^{5} + x^{2} - 14 x^{1000}$
[Opening the brackets]

$= (14 x^{1000} - 14 x^{1000}) + (20 x^{10} y^{5} - 10 x^{10} y^{5}) + (3 y^{1000} - 2 y^{1000} + x^{2})$
[Placing the like terms together]

$= 10 x^{10} y^{5} + y^{1000} + x^{2}$

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