Subtract. $(3x - 4y) - (4x - 3y)$
Answer (2)
The subtraction of the expressions ( 3 x − 4 y ) − ( 4 x − 3 y ) simplifies to − x − y . This is achieved by distributing the negative sign and combining like terms in the expression. The final result is therefore oxed{-x - y} .
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Distribute the negative sign: ( 3 x − 4 y ) − ( 4 x − 3 y ) = 3 x − 4 y − 4 x + 3 y .
Group like terms: 3 x − 4 x − 4 y + 3 y .
Combine like terms: ( 3 x − 4 x ) + ( − 4 y + 3 y ) = − x − y .
The simplified expression is − x − y .
Explanation
Understanding the Problem We are asked to subtract the expression ( 4 x − 3 y ) from ( 3 x − 4 y ) . This involves distributing the negative sign and combining like terms.
Distributing the Negative Sign First, distribute the negative sign to each term inside the second parentheses: ( 3 x − 4 y ) − ( 4 x − 3 y ) = 3 x − 4 y − 4 x + 3 y
Grouping Like Terms Next, group the like terms together: 3 x − 4 x − 4 y + 3 y
Combining Like Terms Now, combine the like terms: ( 3 x − 4 x ) + ( − 4 y + 3 y ) = − x − y
Final Answer Therefore, the simplified expression is − x − y .
Examples
Understanding how to subtract algebraic expressions is crucial in various fields, such as physics and engineering, where you often need to manipulate equations to solve for unknown variables. For example, in circuit analysis, you might need to subtract voltage drops across different components to find the overall voltage in a circuit. Similarly, in mechanics, you might subtract force vectors to find the net force acting on an object. These skills are also useful in economics for analyzing cost and revenue functions.
