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प्रश्न
Take away:
\[\frac{y^3}{3} + \frac{7}{3} y^2 + \frac{1}{2}y + \frac{1}{2} \text { from } \frac{1}{3} - \frac{5}{3} y^2\]
उत्तर
The difference is given by:
\[\left( \frac{1}{3} - \frac{5}{3} y^2 \right) - \left( \frac{y^3}{3} + \frac{7 y^2}{3} + \frac{y}{2} + \frac{1}{2} \right)\]
\[ = \frac{1}{3} - \frac{5}{3} y^2 - \frac{y^3}{3} - \frac{7 y^2}{3} - \frac{y}{2} - \frac{1}{2}\]
\[= \frac{1}{3} - \frac{1}{2} - \frac{y}{2} - \frac{5}{3} y^2 - \frac{7 y^2}{3} - \frac{y^3}{3}\] ( Collecting like terms)
= \[\left( \frac{2 - 3}{6} \right) - \frac{y}{2} + \left( \frac{- 5 - 7}{3} \right) y^2 - \frac{y^3}{3}\]
\[= - \frac{1}{6} - \frac{y}{2} - 4 y^2 - \frac{y^3}{3}\] (Combining like terms. )
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