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Question
Subtract:
\[\frac{2}{3} y^3 - \frac{2}{7} y^2 - 5 \text { from }\frac{1}{3} y^3 + \frac{5}{7} y^2 + y - 2\]
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Solution
\[\left( \frac{1}{3} y^3 + \frac{5}{7} y^2 + y - 2 \right) - \left( \frac{2}{3} y^3 - \frac{2}{7} y^2 - 5 \right)\]
\[ = \frac{1}{3} y^3 + \frac{5}{7} y^2 + y - 2 - \frac{2}{3} y^3 + \frac{2}{7} y^2 + 5\]
\[ = \frac{1}{3} y^3 - \frac{2}{3} y^3 + \frac{5}{7} y^2 + \frac{2}{7} y^2 + y - 2 + 5 (\text { Collecting like terms })\]
\[ = - \frac{1}{3} y^3 + y^2 + y + 3 (\text { Combining like terms })\]
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