Questions: Simplify the expression -(2/5)(10+15 m-20 n).

Simplify the expression -(2/5)(10+15 m-20 n).
Transcript text: Simplify the expression $-\frac{2}{5}(10+15 m-20 n)$.
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Solution

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Solution Steps

Step 1: Distribute the negative sign and the fraction

We start by distributing \(-\frac{2}{5}\) to each term inside the parentheses: \[ -\frac{2}{5}(10 + 15m - 20n) = -\frac{2}{5} \cdot 10 - \frac{2}{5} \cdot 15m + \frac{2}{5} \cdot 20n. \]

Step 2: Perform the multiplication

Multiply each term: \[ -\frac{2}{5} \cdot 10 = -4, \quad -\frac{2}{5} \cdot 15m = -6m, \quad \frac{2}{5} \cdot 20n = 8n. \]

Step 3: Combine the terms

Combine the results from Step 2: \[ -4 - 6m + 8n. \]

Final Answer

The simplified expression is: \[ \boxed{-4 - 6m + 8n}. \]

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