Question

Simplify the following:

\[\left( \frac{1}{3} y^2 - \frac{4}{7}y + 11 \right) - \left( \frac{1}{7}y - 3 + 2 y^2 \right) - \left( \frac{2}{7}y - \frac{2}{3} y^2 + 2 \right)\]

Answer 1

\[\left( \frac{1}{3} y^2 - \frac{4}{7}y + 11 \right) - \left( \frac{1}{7}y - 3 + 2 y^2 \right) - \left( \frac{2}{7}y - \frac{2}{3} y^2 + 2 \right)\]

\[ = \frac{1}{3} y^2 - \frac{4}{7}y + 11 - \frac{1}{7}y + 3 - 2 y^2 - \frac{2}{7}y + \frac{2}{3} y^2 - 2\]

\[= \frac{1}{3} y^2 - 2 y^2 + \frac{2}{3} y^2 - \frac{4}{7}y - \frac{1}{7}y - \frac{2}{7}y + 11 + 3 - 2\]

(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)