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Difficulty: MediumSimplifying Algebraic Expressions

Simplify the following algebraic expression completely:

3(4m−2n)−2(3m+5n)−(m−12n)3(4m - 2n) - 2(3m + 5n) - (m - 12n)

Answer: 5m - 4n / 5m-4n / -4n + 5m / -4n+5m

Answer

5m - 4n
To simplify the expression, first apply the distributive property to eliminate the parentheses, taking care to distribute the negative signs properly: 12m−6n−6m−10n−m+12n12m - 6n - 6m - 10n - m + 12n. Then, combine the like terms for mm (12m−6m−m=5m12m - 6m - m = 5m) and the like terms for nn (−6n−10n+12n=−4n-6n - 10n + 12n = -4n) to reach the final answer of 5m−4n5m - 4n.

Step-by-Step Solution

1
Distribute the coefficients to the terms inside each set of parentheses.
12m−6n−6m−10n−m+12n12m - 6n - 6m - 10n - m + 12n
The distributive property must be applied first to remove parentheses before like terms can be combined.
2
Group the like terms for variables mm and nn.
(12m−6m−m)+(−6n−10n+12n)(12m - 6m - m) + (-6n - 10n + 12n)
Grouping like terms organizes the expression to easily combine their coefficients.
3
Combine the coefficients of the grouped terms.
5m−4n5m - 4n
Evaluating the addition and subtraction of the coefficients yields the fully simplified expression.

Key Concept

Simplifying Algebraic Expressions
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Topics

Simplifying Algebraic Expressions

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