Multiply $(2 x^{2} - 6 x + 10)$ by $(x + y^{2})$ .

2 x^{3} + 12 x^{2} y^{2} - 6 x^{2} - x y^{2} + 10 y^{2} + 10 x

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2 x^{3} + 2 x^{2} y^{2} - 6 x^{2} + 16 x y^{2} + 10 y^{2} + 10 x

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2 x^{3} + 2 x^{2} y^{2} - 6 x^{2} - 6 x y^{2} + 10 y^{2} + 10 x

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2 x^{3} + x^{2} y^{2} - 6 x^{2} - 6 x y^{2} + 10 y^{2}

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Solution

The correct option is C $2 x^{3} + 2 x^{2} y^{2} - 6 x^{2} - 6 x y^{2} + 10 y^{2} + 10 x$
$(2 x^{2} - 6 x + 10) \times (x + y^{2})$
= $x (2 x^{2} - 6 x + 10) + y^{2} (2 x^{2} - 6 x + 10)$
= $2 x^{3} - 6 x^{2} + 10 x + 2 x^{2} y^{2} - 6 x y^{2} + 10 y^{2}$
Rearranging the terms,
$2 x^{3} + 2 x^{2} y^{2} - 6 x^{2} - 6 x y^{2} + 10 y^{2} + 10 x$

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