question_answer

             Find the value of the given expression, if y = 2. \[\left( \frac{1}{3}{{y}^{2}}-\frac{4}{7}y+5 \right)-\left( \frac{2}{7}y-\frac{2}{3}{{y}^{2}}+2 \right)\]

Answer:

\[\left( \frac{1}{3}{{y}^{2}}-\frac{4}{7}y+5 \right)-\left( \frac{2}{7}y-\frac{2}{3}{{y}^{2}}+2 \right)\] \[=\frac{1}{3}{{y}^{2}}-\frac{4}{7}y+5-\frac{2}{7}y+\frac{2}{3}{{y}^{2}}-2\] \[=\left( \frac{1}{3}+\frac{2}{3} \right){{y}^{2}}-\left( \frac{4}{7}+\frac{2}{7} \right)y+5-2\] \[=\frac{3}{3}{{y}^{2}}-\frac{6}{7}y+3\] \[={{y}^{2}}-\frac{6}{7}y+3\] \[={{\left( 2 \right)}^{2}}-\frac{6}{7}y+3\] \[=4-\frac{12}{7}+3\] \[=\frac{28-12+21}{7}\] \[=\frac{37}{7}.\]