Distribute to create an equivalent expression with the fewest symbols possible.

$(6 e-3 f-4) \cdot 2=$

Distribute the constant 2 to each term inside the parentheses.
Multiply each term by 2: 2 × 6 e = 12 e , 2 × ( − 3 f ) = − 6 f , and 2 × ( − 4 ) = − 8 .
Combine the results to form the equivalent expression: 12 e − 6 f − 8 .
The final simplified expression is 12 e − 6 f − 8 ​ .

Explanation

Understanding the Problem We are asked to distribute the constant 2 into the expression ( 6 e − 3 f − 4 ) . This means we need to multiply each term inside the parentheses by 2.

Distributing the Constant Let's distribute the 2 to each term:


2"." ( 6 e − 3 f − 4 ) = 2"." ( 6 e ) − 2"." ( 3 f ) − 2"." ( 4 )

Performing the Multiplication Now, let's perform each multiplication:

2"." ( 6 e ) = 12 e 2"." ( 3 f ) = 6 f 2"." ( 4 ) = 8
So, the expression becomes:
12 e − 6 f − 8

Final Answer The equivalent expression with the fewest symbols is 12 e − 6 f − 8 .

Examples
Imagine you're baking cookies and a recipe calls for ( 6 e − 3 f − 4 ) cups of ingredients, where e represents flour and f represents sugar. If you want to double the recipe, you need to multiply the entire expression by 2. Distributing the 2 ensures you double each ingredient correctly, resulting in 12 e − 6 f − 8 cups of ingredients.

Answered by GinnyAnswer | 2025-07-03

To distribute the expression ( 6 e − 3 f − 4 ) ⋅ 2 , multiply each term inside the parentheses by 2. This results in the equivalent expression 12 e − 6 f − 8 . Thus, the final expression is 12 e − 6 f − 8 .
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Answered by Anonymous | 2025-07-04