Simplifying Mathematical Expressions Step-by-Step

We need to simplify the given mathematical expression using the order of operations (BODMAS/PEMDAS).

The expression is:

$\text{2} \times [4 - \{2 - (\text{2} - \text{3}) - (\text{2} + \text{3})\} - \text{1}] - \text{5} \times [-\text{3} - (\text{3} - \text{2})]$

Let's simplify it step-by-step, working from the innermost brackets outwards.

Step 1: Simplify Innermost Parentheses

First, we evaluate the expressions inside the parentheses:

• $(\text{2} - \text{3}) = -\text{1}$
• $(\text{2} + \text{3}) = \text{5}$
• $(\text{3} - \text{2}) = \text{1}$

Substitute these values back into the expression:

$\text{2} \times [4 - \{2 - (-\text{1}) - (\text{5})\} - \text{1}] - \text{5} \times [-\text{3} - (\text{1})]$

Step 2: Simplify Curly Braces

Next, we simplify the expression inside the curly braces:

• $\{2 - (-\text{1}) - \text{5}\} = \{2 + \text{1} - \text{5}\}$
• $= \{3 - \text{5}\}$
• $= -\text{2}$

Substitute this value back into the expression:

$\text{2} \times [4 - (-\text{2}) - \text{1}] - \text{5} \times [-\text{3} - \text{1}]$

Step 3: Simplify Square Brackets

Now, we simplify the expressions inside the square brackets:

• $[4 - (-\text{2}) - \text{1}] = [4 + \text{2} - \text{1}]$
• $= [6 - \text{1}]$
• $= \text{5}$

And the second bracket:

• $[-\text{3} - \text{1}] = -\text{4}$

Substitute these values back into the expression:

$\text{2} \times [\text{5}] - \text{5} \times [-\text{4}]$

Step 4: Perform Multiplication

Now, perform the multiplications:

• $\text{2} \times \text{5} = \text{10}$
• $\text{5} \times (-\text{4}) = -\text{20}$

Substitute these values back into the expression:

$\text{10} - (-\text{20})$

Step 5: Perform Final Subtraction

Finally, perform the subtraction:

• $\text{10} - (-\text{20}) = \text{10} + \text{20}$
• $= \text{30}$

Thus, the simplified value of the expression is 30.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information on Simplifying Expressions

When simplifying expressions with multiple brackets, it is crucial to follow the correct order of operations. Always start with the innermost grouping symbols (parentheses, then curly braces, then square brackets) and work outwards. Perform operations within each set of brackets in the order of exponents, multiplication/division, and finally addition/subtraction.

Remember that subtracting a negative number is the same as adding a positive number, as seen in the step $\text{10} - (-\text{20}) = \text{10} + \text{20}$.

Careful handling of negative signs is essential throughout the simplification process to avoid errors.