Add $(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})$ and $(5 - 6 y - 8 y^{3} + y^{2})$ .

$- 3 y - 4 y^{2} + 5 y^{3}$

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$- y - 3 y^{2} + 5 y^{3}$

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$- y - 4 y^{2} + 5 y^{3}$

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$- y - 4 y^{2} + 6 y^{3}$

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Solution

The correct option is C
$- y - 4 y^{2} + 5 y^{3}$

To add : $(3 + 2 y - 5 y^{2} + 6 y^{3}), (- 8 + 3 y + 7 y^{3})$ and $(5 - 6 y - 8 y^{3} + y^{2})$

$(- 8 + 3 y + 7 y^{3})$ does not have the term with $y^{2}$ . So, we add $0 y^{2}$ and hence, the expression will be $(- 8 + 3 y + 0 y^{2} + 7 y^{3})$ .

On adding there expressions, we get,
$3 + 2 y - 5 y^{2} + 6 y^{3}$
$- 8 + 3 y + 0 y^{2} + 7 y^{3}$
$5 - 6 y + y^{2} - 8 y^{3} - -------------------- -$
$- 1 y - 4 y^{2} + 5 y^{3}$

$(3 + 2 y - 5 y^{2} + 6 y^{3}) + (- 8 + 3 y + 7 y^{3}) + (5 - 6 y - 8 y^{3} + y^{2}) = (- y - 4 y^{2} + 5 y^{3})$

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Adding $3 + 2 y - 5 y^{2} + 6 y^{3}, - 8 + 3 y + 7 y^{3}$ and $5 - 6 y - 8 y^{3} + y^{2}$ , we get

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