3. Раскройте скобки и приведите подобные слагаемые: 1) 8(6a - 7) - 17a; 2) 6b - 7(12 - 3b); 3) 1,6(c - 8) + 0,4(8 - 3c); 4) 1,6(9a - 3b) - (4b - 6a) · 1,5; 5) -(5,7m - 6,7) - (7,9 - 3,6m); 6) \(\frac{15}{16}\)\(\frac{5}{3}x - \frac{4}{15}y\) - \(\frac{7}{23}\)\(3\frac{2}{7}x - 2\frac{4}{21}y\).

Question

Accepted Answer

\( 8(6a - 7) - 17a = 8 \cdot 6a - 8 \cdot 7 - 17a = 48a - 56 - 17a = (48a - 17a) - 56 = 31a - 56 \)
\( 6b - 7(12 - 3b) = 6b - 7 \cdot 12 - 7 \cdot (-3b) = 6b - 84 + 21b = (6b + 21b) - 84 = 27b - 84 \)
\( 1,6(c - 8) + 0,4(8 - 3c) = 1,6c - 1,6 \cdot 8 + 0,4 \cdot 8 - 0,4 \cdot 3c = 1,6c - 12,8 + 3,2 - 1,2c = (1,6c - 1,2c) + (-12,8 + 3,2) = 0,4c - 9,6 \)
\( 1,6(9a - 3b) - (4b - 6a) \cdot 1,5 = 1,6 \cdot 9a - 1,6 \cdot 3b - (4b \cdot 1,5 - 6a \cdot 1,5) = 14,4a - 4,8b - (6b - 9a) = 14,4a - 4,8b - 6b + 9a = (14,4a + 9a) + (-4,8b - 6b) = 23,4a - 10,8b \)
\( -(5,7m - 6,7) - (7,9 - 3,6m) = -5,7m + 6,7 - 7,9 + 3,6m = (-5,7m + 3,6m) + (6,7 - 7,9) = -2,1m - 1,2 \)
\( \frac{15}{16}(\frac{5}{3}x - \frac{4}{15}y) - \frac{7}{23}(3\frac{2}{7}x - 2\frac{4}{21}y) = \frac{15}{16} \cdot \frac{5}{3}x - \frac{15}{16} \cdot \frac{4}{15}y - \frac{7}{23}(\frac{23}{7}x - \frac{46}{21}y) = \frac{25}{16}x - \frac{1}{4}y - (\frac{7}{23} \cdot \frac{23}{7}x - \frac{7}{23} \cdot \frac{46}{21}y) = \frac{25}{16}x - \frac{1}{4}y - (x - \frac{2}{3}y) = \frac{25}{16}x - \frac{1}{4}y - x + \frac{2}{3}y = (\frac{25}{16}x - x) + (-\frac{1}{4}y + \frac{2}{3}y) = (\frac{25}{16}x - \frac{16}{16}x) + (-\frac{3}{12}y + \frac{8}{12}y) = \frac{9}{16}x + \frac{5}{12}y \)

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