Use the distributive property to simplify the expression.
8(3x+4)
Answer (1)
Apply the distributive property: 8 ( 3 x + 4 ) = 8 ( 3 x ) + 8 ( 4 ) .
Multiply: 8 ( 3 x ) = 24 x and 8 ( 4 ) = 32 .
Combine the terms: 24 x + 32 .
The simplified expression is 24 x + 32 .
Explanation
Understanding the Problem We are given the expression 8 ( 3 x + 4 ) and asked to simplify it using the distributive property. The distributive property states that a ( b + c ) = ab + a c . In this case, we have a = 8 , b = 3 x , and c = 4 .
Applying the Distributive Property Applying the distributive property, we multiply 8 by each term inside the parentheses: 8 ( 3 x + 4 ) = 8 ( 3 x ) + 8 ( 4 )
Performing the Multiplications Now, we perform the multiplications: 8 ( 3 x ) = 24 x and 8 ( 4 ) = 32
Combining the Terms Finally, we combine the terms to get the simplified expression: 24 x + 32
Final Answer Therefore, the simplified expression is 24 x + 32 .
Examples
The distributive property is useful in everyday situations, such as calculating the total cost of multiple items. For example, if you buy 8 items that each cost $3 plus a $4 shipping fee, the total cost can be calculated as 8 ( 3 + 4 ) . Using the distributive property, this becomes $8 3 + 8 4 = 24 + 32 = $56. This shows how the distributive property helps break down complex calculations into simpler steps.
