Simplify the following expression: $-y(3 z-2 m)$
Answer (2)
To simplify the expression − y ( 3 z − 2 m ) , we distribute the − y to both terms inside the parentheses, resulting in − 3 yz + 2 m y . Therefore, the simplified expression is − 3 yz + 2 m y .
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Distribute − y to both terms inside the parentheses: − y ( 3 z − 2 m ) .
Multiply − y by 3 z and − 2 m : − y ( 3 z ) − y ( − 2 m ) .
Simplify the expression: − 3 yz + 2 m y .
The simplified expression is 2 m y − 3 yz .
Explanation
Understanding the Expression We are given the expression − y ( 3 z − 2 m ) and asked to simplify it. This involves distributing the − y term to both terms inside the parentheses.
Distributing and Simplifying To simplify the expression, we distribute − y to both 3 z and − 2 m :
− y ( 3 z − 2 m ) = − y ( 3 z ) − y ( − 2 m ) = − 3 yz + 2 y m So, the simplified expression is − 3 yz + 2 y m .
Final Answer The simplified form of the expression − y ( 3 z − 2 m ) is − 3 yz + 2 m y .
Examples
Understanding how to expand and simplify algebraic expressions like this is fundamental in many areas, such as physics and engineering. For example, in physics, you might use this to calculate the force on an object, where y represents time, z represents velocity, and m represents mass. The expression could represent a simplified model of how force changes over time. In economics, similar expressions can model cost functions or revenue streams, where variables represent quantities or prices. Simplifying these expressions allows for easier analysis and decision-making.
