Simplify.
$3(4 x-5 y)+2 y$
Answer (2)
Distribute the constant: Multiply 3 by each term inside the parentheses, resulting in 12 x − 15 y .
Combine like terms: Add the y terms, − 15 y + 2 y = − 13 y .
Simplify the expression: Combine the results to get 12 x − 13 y .
State the final answer: The simplified expression is 12 x − 13 y .
Explanation
Understanding the Problem We are asked to simplify the expression 3 ( 4 x − 5 y ) + 2 y . This involves distributing the 3 across the terms inside the parentheses and then combining like terms.
Distributing the Constant First, distribute the 3 into the parentheses:
3 ( 4 x − 5 y ) = 3 × 4 x − 3 × 5 y = 12 x − 15 y
So the expression becomes:
12 x − 15 y + 2 y
Combining Like Terms Next, combine the like terms, which are the terms involving y :
− 15 y + 2 y = ( − 15 + 2 ) y = − 13 y
So the simplified expression is:
12 x − 13 y
Final Answer Therefore, the simplified expression is 12 x − 13 y .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and is used in various real-life situations. For example, suppose you are planning a rectangular garden where the length is 4 x − 5 y feet and you want to put a fence around it. If you decide to increase the length by 2y feet, the total length of the fence needed can be represented by 3 ( 4 x − 5 y ) + 2 y . Simplifying this expression helps you determine the exact amount of fencing material you need, ensuring you don't buy too much or too little.
To simplify the expression 3 ( 4 x − 5 y ) + 2 y , first distribute the 3 to get 12 x − 15 y + 2 y . Then, combine like terms to arrive at 12 x − 13 y . The final simplified expression is 12 x − 13 y .
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