Expand the expression. $2(1.5 u-2.3)$
Answer (2)
To expand the expression 2 ( 1.5 u − 2.3 ) , use the distributive property to multiply 2 by both 1.5 u and − 2.3 . This leads to the final result of 3 u − 4.6 .
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Distribute the 2 to both terms inside the parentheses: 2 ( 1.5 u ) − 2 ( 2.3 ) .
Multiply the constants: 2 × 1.5 = 3 and 2 × 2.3 = 4.6 .
Write the expanded expression: 3 u − 4.6 .
The final expanded expression is 3 u − 4.6 .
Explanation
Understanding the Problem We are asked to expand the expression 2 ( 1.5 u − 2.3 ) . This involves distributing the 2 to both terms inside the parentheses.
Applying the Distributive Property We apply the distributive property: 2 ( 1.5 u − 2.3 ) = 2 × ( 1.5 u ) − 2 × ( 2.3 ) .
Multiplying the Constants Now, we multiply the constants. First, 2 × 1.5 = 3 , so 2 × ( 1.5 u ) = 3 u . Next, 2 × 2.3 = 4.6 .
Writing the Expanded Expression Therefore, the expanded expression is 3 u − 4.6 .
Final Answer The expanded form of the expression 2 ( 1.5 u − 2.3 ) is 3 u − 4.6 .
Examples
Understanding how to expand expressions like this is useful in many real-life situations. For example, if you're buying multiple items at a store, each with a price that includes tax, you can use the distributive property to calculate the total cost. If you buy 2 items that cost $1.50 each, plus a fixed surcharge of $2.30, the total cost is 2 ( 1.50 + 2.30 ) . Expanding this gives $2(1.50) + 2(2.30) = 3 + 4.60 = $7.60. This helps you quickly calculate costs and understand how each component contributes to the final price.
