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Question
Simplify the following:
\[\left( \frac{1}{3} y^2 - \frac{4}{7}y + 11 \right) - \left( \frac{1}{7}y - 3 + 2 y^2 \right) - \left( \frac{2}{7}y - \frac{2}{3} y^2 + 2 \right)\]
Solution
\[\left( \frac{1}{3} y^2 - \frac{4}{7}y + 11 \right) - \left( \frac{1}{7}y - 3 + 2 y^2 \right) - \left( \frac{2}{7}y - \frac{2}{3} y^2 + 2 \right)\]
\[ = \frac{1}{3} y^2 - \frac{4}{7}y + 11 - \frac{1}{7}y + 3 - 2 y^2 - \frac{2}{7}y + \frac{2}{3} y^2 - 2\]
\[= \frac{1}{3} y^2 - 2 y^2 + \frac{2}{3} y^2 - \frac{4}{7}y - \frac{1}{7}y - \frac{2}{7}y + 11 + 3 - 2\]
(Collecting like terms)
= \[\left( \frac{1 - 6 + 2}{3} \right) y^2 + \left( \frac{- 4 - 1 - 2}{7} \right)y + 12\]
\[= - y^2 - 7y + 12\] (Combining like terms)
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