$-6(-8 x+5 y+3 z)$

Apply the distributive property.
$-6(-8 x+5 y+3 z)=-6(-8 x)+\square(5 y)+\square(3 z)$

To expand − 6 ( − 8 x + 5 y + 3 z ) , we apply the distributive property by multiplying − 6 with each term inside the parentheses. This results in 48 x − 30 y − 18 z , and both missing coefficients in the expression are − 6 .
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Answered by Anonymous | 2025-07-04

Apply the distributive property: − 6 ( − 8 x + 5 y + 3 z ) = ( − 6 ) ( − 8 x ) + ( − 6 ) ( 5 y ) + ( − 6 ) ( 3 z ) .
Calculate each term: ( − 6 ) ( − 8 x ) = 48 x , ( − 6 ) ( 5 y ) = − 30 y , ( − 6 ) ( 3 z ) = − 18 z .
The expanded expression is: − 6 ( − 8 x + 5 y + 3 z ) = 48 x − 30 y − 18 z .
The missing coefficients are -6 and -6, so − 6 ( − 8 x + 5 y + 3 z ) = − 6 ( − 8 x ) + ( − 6 ) ( 5 y ) + ( − 6 ) ( 3 z ) . The final answer is − 6 ​ .

Explanation

Understanding the Problem We are given the expression − 6 ( − 8 x + 5 y + 3 z ) and asked to apply the distributive property to expand it. The distributive property states that a ( b + c + d ) = ab + a c + a d . In this case, we have − 6 ( − 8 x + 5 y + 3 z ) , so we need to multiply − 6 by each term inside the parentheses.

Applying the Distributive Property Applying the distributive property, we have: − 6 ( − 8 x + 5 y + 3 z ) = ( − 6 ) ( − 8 x ) + ( − 6 ) ( 5 y ) + ( − 6 ) ( 3 z ) Now, we multiply each term:

Calculating Each Term ( − 6 ) ( − 8 x ) = 48 x ( − 6 ) ( 5 y ) = − 30 y ( − 6 ) ( 3 z ) = − 18 z So, the expanded expression is: − 6 ( − 8 x + 5 y + 3 z ) = 48 x − 30 y − 18 z

Finding the Missing Coefficients The original expression was given as − 6 ( − 8 x + 5 y + 3 z ) = − 6 ( − 8 x ) + □ ( 5 y ) + □ ( 3 z ) . Comparing this to our expanded expression 48 x − 30 y − 18 z , we can see that the missing terms are − 6 and − 6 . Therefore, the expression becomes: − 6 ( − 8 x + 5 y + 3 z ) = − 6 ( − 8 x ) + ( − 6 ) ( 5 y ) + ( − 6 ) ( 3 z ) − 6 ( − 8 x + 5 y + 3 z ) = 48 x − 30 y − 18 z

Final Answer The missing numbers are both − 6 . Thus, the expression is: − 6 ( − 8 x + 5 y + 3 z ) = − 6 ( − 8 x ) + ( − 6 ) ( 5 y ) + ( − 6 ) ( 3 z ) Therefore, the answer is − 6 and − 6 .


Examples
The distributive property is a fundamental concept in algebra and is used in many real-world applications. For example, suppose you are buying 3 items at a store. Each item costs x dollars, and there is a sales tax of 7%. The total cost can be calculated as 1.07 ( 3 x ) = 3.21 x . This shows how the distributive property helps in calculating the total cost by distributing the tax across all items. Another example is calculating the area of a rectangle with sides ( a + b ) and c , which is c ( a + b ) = a c + b c .

Answered by GinnyAnswer | 2025-07-04