Question

Simplify:

(i) (5x −9y) − (−7x + y)
(ii) $\left(x^2-x\right)-\frac{1}{2}\left(x-3+3x^2\right)$
(iii) [7 − 2x + 5y − (x − y)] − (5x + 3y − 7)
(iv) $\left(\frac{1}{3}{y}^2-\frac{4}{7}y+5\right)-\left(\frac{2}{7}y-\frac{2}{3}{y}^2+2\right)-\left(\frac{1}{7}y-3+2y^2\right)$

Answer 1

Collecting like terms and adding them:

(i) 5x + 7x - 9y -y
= 12x -10y

(ii)
$$\begin{gathered} x^2-\frac{3}{2}{x}^2-x-\frac{1}{2}x+\frac{3}{2} \\ =-\frac{1}{2}{x}^2-\frac{3}{2}x+\frac{3}{2} \end{gathered}$$

(iii) 7 + 7 - 2x -x - 5x + 5y + y - 3y
= 14 - 8x -3y

(iv)
$$\begin{gathered} \frac{1}{3}{\mathrm{y}}^2+\frac{2}{3}{\mathrm{y}}^2-2{\mathrm{y}}^2-\frac{4}{7}\mathrm{y}-\frac{2}{7}\mathrm{y}-\frac{1}{7}\mathrm{y}+5-2+3 \\ =-{\mathrm{y}}^2-\mathrm{y}+6 \end{gathered}$$