5.61 Приведите подобные слагаемые: a) 20x + y 20y x; б) -4b + 5a + 4b + 5a; в) -9с + 4,8n + 4c + 4n; г) 5,3m + 4,7m - 7,1x + 25x; д) \frac{3}{4}z^2 – \frac{4}{9}y + \frac{7}{22}z^2 + \frac{2}{3}y;

Решение:

• а) 20x + y - 20y - x = (20x - x) + (y - 20y) = (20 - 1)x + (1 - 20)y = 19x - 19y
• б) -4b + 5a + 4b + 5a = (5a + 5a) + (-4b + 4b) = (5 + 5)a + (-4 + 4)b = 10a + 0b = 10a
• в) -9с + 4,8n + 4c + 4n = (-9c + 4c) + (4,8n + 4n) = (-9 + 4)c + (4,8 + 4)n = -5c + 8,8n
• г) 5,3m + 4,7m - 7,1x + 25x = (5,3m + 4,7m) + (-7,1x + 25x) = (5,3 + 4,7)m + (-7,1 + 25)x = 10m + 17,9x
• д) \(\frac{3}{4}z^2 – \frac{4}{9}y + \frac{7}{22}z^2 + \frac{2}{3}y\) = (\(\frac{3}{4}z^2 + \frac{7}{22}z^2\)) + (\(-\frac{4}{9}y + \frac{2}{3}y\)) = (\(\frac{3 \cdot 11}{4 \cdot 11}z^2 + \frac{7 \cdot 2}{22 \cdot 2}z^2\)) + (\(-\frac{4}{9}y + \frac{2 \cdot 3}{3 \cdot 3}y\)) = (\(\frac{33}{44}z^2 + \frac{14}{44}z^2\)) + (\(-\frac{4}{9}y + \frac{6}{9}y\)) = \(\frac{47}{44}z^2 + \frac{2}{9}y\) = \(\frac{47}{44}z^2 + \frac{2}{9}y\)

Ответы: 19x - 19y; 10a; -5c + 8,8n; 10m + 17,9x; \(\frac{47}{44}z^2 + \frac{2}{9}y\)