To simplify the expression \(-3y + 7y + 4y^3 - 2y^2 + 6y^3 - 7y^3 - 5y\), we will combine like terms.
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Combine the \(y\) terms: \[ -3y + 7y - 5y = (-3 + 7 - 5)y = -1y \quad \text{or simply} \quad -y \]
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Combine the \(y^2\) terms: \[ -2y^2 \quad \text{(there are no other } y^2 \text{ terms)} \]
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Combine the \(y^3\) terms: \[ 4y^3 + 6y^3 - 7y^3 = (4 + 6 - 7)y^3 = 3y^3 \]
Now, putting all the combined terms together, we have:
\[ 3y^3 - 2y^2 - y \]
So, the simplified expression is:
\[ 3y^3 - 2y^2 - y \]