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Substitution is a technique used in algebra to make solving expressions easier. It involves replacing variables with actual numbers. In our exercise, we need to substitute specific values for the variables given. Here, we're substituting \( m = -4 \) and \( n = -5 \) into the expression \( 8(3m - 5n) \).
- First, identify which variables need values replaced. - Then, plug in the numbers provided into the spots where the variables are.
For instance, when we substitute:\[ m = -4 \text{ and } n = -5\], the expression \( 3m \) becomes \( 3(-4) \) and \( 5n \) becomes \( 5(-5) \). This initial step is crucial as it sets the foundation for working with fixed numbers instead of unknown variables, enabling us to perform subsequent arithmetic calculations with ease.

Arithmetic operations, essentially are the basic calculations like addition, subtraction, multiplication, and division. Once we've substituted the values, our next task is to carry out the arithmetic operations within the expression.
- Focus on the operations inside the parentheses first. - We have two multiplication operations: \( 3(-4) \) and \( 5(-5) \).
Calculating these gives: \( 3 \times -4 = -12 \) and \( 5 \times -5 = -25 \). With these results, our expression transitions to \( 8(-12 + 25) \).
Getting the multiplication right ensures you're accurately combining numbers according to the mathematical rules, leading to the correct intermediate results from which to further simplify.

Simplification is the way we reduce expressions to their simplest forms. It's the last step in solving an expression like ours. We aim to make expressions easy to read and interpret.
- Start by handling operations inside any parentheses. - Simplify the expression step by step, without skipping any calculations.
In our example, we simplify \(-12 + 25\), which results in \(13\). The expression now becomes simpler: \(8 \times 13\).
Carrying out the multiplication gives us a final result: \(8 \times 13 = 104\).
Simplifying correctly helps ensure the expression is accurate and concise. It makes interpreting or using the result straightforward, confirming all calculations align correctly throughout the process.