Simplify:
$-(3 a+4 b)+5 a-4 b$
A. $8 a-8 b$
B. $2 a+8 b$
C. $2 a$
D. $2 a-8 b$
Answer (1)
Distribute the negative sign: − ( 3 a + 4 b ) = − 3 a − 4 b .
Combine like terms: − 3 a + 5 a = 2 a and − 4 b − 4 b = − 8 b .
The simplified expression is 2 a − 8 b .
The equivalent expression from the list is 2 a − 8 b .
Explanation
Understanding the Problem We are given the expression − ( 3 a + 4 b ) + 5 a − 4 b and a list of expressions: 8 a − 8 b , 2 a + 8 b , 2 a , 2 a − 8 b . Our goal is to simplify the given expression and determine which of the expressions in the list is equivalent to the simplified expression.
Distributing the Negative Sign First, we simplify the given expression by distributing the negative sign and combining like terms:
− ( 3 a + 4 b ) + 5 a − 4 b = − 3 a − 4 b + 5 a − 4 b
Combining Like Terms Now, we combine the like terms (terms with the same variable):
( − 3 a + 5 a ) + ( − 4 b − 4 b ) = 2 a − 8 b
Comparing to the List We now have the simplified expression 2 a − 8 b . We need to compare this to the list of expressions provided to find the equivalent one. The list of expressions is:
8 a − 8 b
2 a + 8 b
2 a
2 a − 8 b
Finding the Equivalent Expression By comparing our simplified expression 2 a − 8 b to the list, we can see that it is identical to the fourth expression in the list. Therefore, the equivalent expression is 2 a − 8 b .
Final Answer Therefore, the simplified expression − ( 3 a + 4 b ) + 5 a − 4 b is equivalent to 2 a − 8 b .
Examples
In real-world scenarios, simplifying algebraic expressions is crucial in various fields such as engineering, physics, and economics. For instance, when calculating the total cost of materials in a construction project, you might have an expression involving multiple variables representing the quantities and prices of different materials. Simplifying this expression allows for easier computation and better cost management. Similarly, in physics, simplifying equations helps in analyzing complex systems and making accurate predictions. This skill is also valuable in everyday tasks like budgeting and financial planning, where simplifying expressions can help in understanding and managing expenses effectively.
