$9x - 3y - 5y - 5x - x + 2y
Answer (2)
Group like terms: Identify and group terms with the same variable.
Combine x terms: 9 x − 5 x − x = 3 x .
Combine y terms: − 3 y − 5 y + 2 y = − 6 y .
Write the simplified expression: 3 x − 6 y .
Explanation
Understanding the Expression We are given the expression 9 x − 3 y − 5 y − 5 x − x + 2 y and our goal is to simplify it by combining like terms. This involves identifying terms with the same variable (either x or y ) and then adding or subtracting their coefficients.
Combining x Terms First, let's group the terms with x : 9 x − 5 x − x . We can rewrite this as ( 9 − 5 − 1 ) x . Now, let's calculate the coefficient: 9 − 5 − 1 = 4 − 1 = 3 . So, the combined x term is 3 x .
Combining y Terms Next, let's group the terms with y : − 3 y − 5 y + 2 y . We can rewrite this as ( − 3 − 5 + 2 ) y . Now, let's calculate the coefficient: − 3 − 5 + 2 = − 8 + 2 = − 6 . So, the combined y term is − 6 y .
Simplified Expression Finally, we combine the simplified x and y terms to get the simplified expression: 3 x − 6 y .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with applications in various fields. For example, in physics, you might need to simplify an expression representing the net force acting on an object. If the force in the x-direction is given by F x = 5 x − 2 y and another force in the x-direction is given by G x = − 2 x + y , the total force in the x-direction is F x + G x = ( 5 x − 2 y ) + ( − 2 x + y ) . Simplifying this expression gives 3 x − y , which represents the net force. This skill is also crucial in economics, computer science, and engineering for modeling and solving real-world problems.
To simplify the expression 9 x − 3 y − 5 y − 5 x − x + 2 y , we combine like terms. This results in 3 x − 6 y . The final simplified expression is (\boxed{3x - 6y}.
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