Question

Упростите выражения, выполняя равносильные преобразования: a) -((17a 12b) - (5а - 7b)) - ((14b - 9a) - (15а + 8b)); б) 4m + 6n - (7n - 2(3m + 5n)) - (6m - (5n - 2m)) - (4m + 8n).​

Answer 1

Пошаговое объяснение:

а)

в первой скобке пропущен знак между 17а и 12b

б)

4m + 6n - (7n - 2(3m + 5n)) - (6m - (5n - 2m)) - (4m + 8n) =

4m + 6n - (7n - 6m - 10n) - (6m - 5n + 2m) - (4m + 8n) =

4m + 6n - 7n + 6m + 10n - 6m + 5n - 2m - 4m - 8n =

(4m + 6m - 6m - 2m - 4m) + (6n - 7n + 10n + 5n - 8n) = -2m + 6n

Answer 2

a) -((17a + 12b) - (5a - 7b)) - ((14b - 9a) - (15a + 8b))

First, let's simplify the expressions inside the parentheses:

(17a + 12b) - (5a - 7b) = 17a + 12b - 5a + 7b = 12a + 19b (14b - 9a) - (15a + 8b) = 14b - 9a - 15a - 8b = -9a - a6b

Now, we substitute these simplified expressions back into the original equation:

-((12a + 19b) - (9a + 16b)) - (-9a - 16b) = -12a - 19b + 9a + 16b + 9a + 16b = -12a + 9a + 9a - 19b + 16b + 16b = 6a + 13b

Therefore, the simplified expression is 6a + 13b.

b) 4m + 6n - (7n - 2(3m + 5n)) - (6m - (5n - 2m)) - (4m + 8n)

Let's simplify the expressions inside the parentheses:

7n - 2(3m + 5n) = 7n - 6m - 10n = -6m - 3n 5n - 2m = -2m + 5n

Now, we substitute these simplified expressions back into the original equation:

4m + 6n - (-6m - 3n) - (6m - (-2m + 5n)) - (4m + 8n) = 4m + 6n + 6m + 3n - 6m + 2m - 5n - 4m - 8n = (4m - 6m + 6m - 2m) + (6n + 3n - 5n - 8n) = 2m - 4n

Therefore, the simplified expression is 2m - 4n.