Question

1) а - (b - (с - (a - b))) + (-с — (а - (a + с))) - с; 2) x+ (у - (х - (2 - у))) - (2 - (-х — (х – у))) - у.​

Answer 1

Ответ:

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Answer 2

Let's simplify the given expressions step by step:

1. а - (b - (с - (a - b))) + (-с — (а - (a + с))) - с;

Step 1: Start from the innermost parentheses and work your way out.

• Inside the innermost parentheses, a - b.
• So, с - (a - b) becomes с - a + b.

Step 2:

• Now, we have b - (с - (с - a + b)) inside the next set of parentheses.
• c - (c - a + b) simplifies to c - c + a - b, which simplifies to a - b.

Step 3:

• We have a - (a - b) inside the next set of parentheses.
• a - (a - b) simplifies to a - a + b, which simplifies to b.

Step 4:

• The expression now becomes a - b + (-с — (b)).

Step 5:

• Finally, we have -с — (b), which simplifies to -с + (-b).

Step 6:

• The expression becomes a - b - с - b.

Step 7:

• Combining like terms, we get a - b - b - с, which can be simplified to a - 2b - с.

So, the simplified expression is: a - 2b - с.

2. x + (у - (х - (2 - у))) - (2 - (-х — (х – у))) - у.

Step 1:

• Inside the innermost parentheses, х - у.
• So, (у - (х - (2 - у))) becomes (у - (2 - у)).

Step 2:

• (у - (2 - у)) simplifies to у - 2 + у, which is 2у - 2.

Step 3:

• Inside the next set of parentheses, -х — (х – у) simplifies to -х - х + у, which is -2х + у.

Step 4:

• The expression now becomes x + (2у - 2) - (2 - (-2х + у)) - у.

Step 5:

• (-2х + у) simplifies to -2х + у.

Step 6:

• The expression becomes x + (2у - 2) - (2 + 2х - у) - у.

Step 7:

• Distribute the negative sign inside the second set of parentheses: x + (2у - 2) - 2 - 2х + у - у.

Step 8:

• Combine like terms: x - 2х + 2у - у - у - 2.

Step 9:

• Combine like terms further: (x - 2х) + (2у - у - у) - 2.

Step 10:

• Simplify: -х + y - 2у - 2.

So, the simplified expression is: -х + y - 2у - 2.