Question
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1. Expand to write an equivalent expression: \( -\frac{1}{2}(-2 x+4 y) \) Type the answer in the box below. 2. Factor to write an equivalent expression: \( 26 a-10 \) Type the answer in the box below

Ask by Kelly Dickson. in the United States
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

1. \( x - 2y \) 2. \( 2(13a - 5) \)

Solution

1. Expand to write an equivalent expression for \( -\frac{1}{2}(-2x+4y) \): - Distribute the multiplication: \[ -\frac{1}{2}(-2x) = x \quad \text{and} \quad -\frac{1}{2}(4y) = -2y \] - Thus, the expanded expression is: \[ x-2y \] 2. Factor to write an equivalent expression for \( 26a-10 \): - Notice that both terms are even, so factor out the greatest common factor \(2\): \[ 26a-10 = 2(13a-5) \] The final answers are: 1. \( x-2y \) 2. \( 2(13a-5) \)

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The Deep Dive

When you expand \( -\frac{1}{2}(-2x + 4y) \), you distribute the \( -\frac{1}{2} \) to each term inside the parentheses. This gives you \( x - 2y \). The negative signs cancel out, leaving you with a positive outcome! To factor \( 26a - 10 \), look for the greatest common factor in both terms. In this case, the GCF is 2. By factoring it out, you get \( 2(13a - 5) \). This simplified form makes it easier to handle in equations or further calculations!

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