Question

Simplify $(\frac{1}{3}{y}^2-\frac{4}{7}y+5)-(\frac{2}{7}y-\frac{2}{3}{y}^2+2)-(\frac{1}{7}y-3+2y^2)$

Answer 1

Given expression is

$(\frac{1}{3}{y}^2-\frac{4}{7}y+5)-(\frac{2}{7}y-\frac{2}{3}{y}^2+2)-(\frac{1}{7}y-$$3+2y^2)$
$=(\frac{1}{3}{y}^2-\frac{4}{7}y+5)-\frac{2}{7}y+\frac{2}{3}{y}^2-2-\frac{1}{7}y+3-2y^2$

Grouping $y^2,y$ and constant terms as

$=(\frac{1}{3}+\frac{2}{3}-2)y^2-(\frac{4}{7}+\frac{2}{7}+\frac{1}{7})y+5-2+3$

$=\left(\frac{1+2-6}{3}\right)y^2-\left(\frac{4+2+1}{7}\right)y+6$
$=\left(\frac{-3}{3}\right)y^2-\left(\frac{7}{7}\right)y+6$
$=-y^2-\left(1\right)y+6$

Hence, the value of the given expression is $-y^2-y+6$