Use the distributive property to remove the parentheses.
$-3(3x-4y-6)$

To remove the parentheses from the expression − 3 ( 3 x − 4 y − 6 ) , we apply the distributive property. This leads to the simplified expression − 9 x + 12 y + 18 . Each term is multiplied by − 3 and combined to achieve the final result.
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Answered by Anonymous | 2025-07-04

Distribute -3 to each term inside the parentheses: − 3 ( 3 x − 4 y − 6 ) = ( − 3 ) ( 3 x ) + ( − 3 ) ( − 4 y ) + ( − 3 ) ( − 6 ) .
Multiply each term: ( − 3 ) ( 3 x ) = − 9 x , ( − 3 ) ( − 4 y ) = 12 y , ( − 3 ) ( − 6 ) = 18 .
Combine the simplified terms: − 9 x + 12 y + 18 .
The final expression is: − 9 x + 12 y + 18 ​ .

Explanation

Understanding the Problem We are asked to remove the parentheses from the expression − 3 ( 3 x − 4 y − 6 ) using the distributive property. The distributive property states that a ( b + c ) = ab + a c . We will apply this property to each term inside the parentheses.

Applying the Distributive Property We distribute the − 3 to each term inside the parentheses: − 3 ( 3 x − 4 y − 6 ) = ( − 3 ) ( 3 x ) + ( − 3 ) ( − 4 y ) + ( − 3 ) ( − 6 ) Now, we simplify each term:

Simplifying Each Term ( − 3 ) ( 3 x ) = − 9 x ( − 3 ) ( − 4 y ) = 12 y ( − 3 ) ( − 6 ) = 18 So, we have:

Combining the Terms − 9 x + 12 y + 18 Thus, the expression with the parentheses removed is − 9 x + 12 y + 18 .


Examples
The distributive property is useful in many real-life situations. For example, suppose you are buying 3 bags of apples, each containing 3 red apples, 4 green apples, and 6 yellow apples. Using the distributive property, you can calculate the total number of each type of apple: 3 ( 3 + 4 + 6 ) = 3 ( 3 ) + 3 ( 4 ) + 3 ( 6 ) = 9 + 12 + 18 = 39 apples in total. This shows how the distributive property helps in simplifying calculations involving groups of items.

Answered by GinnyAnswer | 2025-07-04