Math Problem Statement

(3m-6n)-(2n+3m)+(2m-4n)

Solution

To simplify the expression (3m6n)(2n+3m)+(2m4n)(3m-6n)-(2n+3m)+(2m-4n), follow these steps:

  1. Distribute the negative sign through the parentheses.
  2. Combine like terms.

Step 1: Distribute the negative sign

(3m6n)(2n+3m)+(2m4n)(3m - 6n) - (2n + 3m) + (2m - 4n)

Distribute the negative sign to the second group:

(3m6n)2n3m+(2m4n)(3m - 6n) - 2n - 3m + (2m - 4n)

Step 2: Combine like terms

Group the mm terms together and the nn terms together:

(3m3m+2m)+(6n2n4n)(3m - 3m + 2m) + (-6n - 2n - 4n)

Combine the mm terms:

(3m3m+2m)=2m(3m - 3m + 2m) = 2m

Combine the nn terms:

(6n2n4n)=12n(-6n - 2n - 4n) = -12n

So, the simplified expression is:

2m12n2m - 12n

Do you want more details or have any questions about this process?

Here are 5 numbered questions you can ask:

  1. How do you simplify algebraic expressions with multiple variables?
  2. What are like terms in algebra?
  3. How do you solve linear equations?
  4. Can you explain the distributive property in algebra?
  5. How do you factor quadratic equations?

Tip: Always combine like terms to simplify algebraic expressions effectively.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9