Unità 6 - Polinomi

Determina la somma e la differenza dei polinomi delle seguenti coppie.

$-0.2x + 0.3y - 0.5$ , $\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2}$

$(-0.2x+0.3y-0.5) + (\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})$ $=$ $(-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2})+(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})$ $=$ $-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2}+\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2}$ $=$ $(\dfrac{2}{5}x-\dfrac{1}{5}x)$ $+$ $(\dfrac{3}{10}y+\dfrac{3}{2}y)$ $+$ $(-\dfrac{1}{2}-\dfrac{1}{2})$ $=$ $\dfrac{1}{5}x+\dfrac{3+15}{10}y+(-\dfrac{2}{2})$ $=$ $\dfrac{1}{5}x+\dfrac{\cancel{18}}{\cancel{10}}y+(-1)$ $=$ $\dfrac{1}{5}x+\dfrac{9}{5}y-1$
$(-0.2x+0.3y-0.5)-(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})$ $=$ $(-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2})-(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})$ $=$ $-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2}-\dfrac{2}{5}x-\dfrac{3}{2}y+\dfrac{1}{2}$ $=$ $(-\dfrac{1}{5}x-\dfrac{2}{5}x)$ $+$ $(\dfrac{3}{10}y-\dfrac{3}{2}y)$ $+$ $(\dfrac{1}{2}-\dfrac{1}{2})$ $=$ $-\dfrac{3}{5}x+\dfrac{3-15}{10}y$ $=$ $-\dfrac{3}{5}x+(-\dfrac{\cancel{12}}{\cancel{10}}y)$ $=$ $-\dfrac{3}{5}x-\dfrac{6}{5}y$