Choose the properties that can be used to rewrite \( 2(a+5)-4 \) as \( 2 a+6 \). \[ \begin{aligned} 2(a+5)-4 & =2 \cdot a+2 \cdot 5-4 \\ & =2 a+10-4 \\ & =2 a+(10-4) \end{aligned} \] distributive property distributive property commutative property associative property

To rewrite \( 2(a+5)-4 \) as \( 2a + 6 \), the following properties are used: 1. **Distributive Property**: \[ 2(a+5) - 4 = 2 \cdot a + 2 \cdot 5 - 4 = 2a + 10 - 4 \] This step applies the distributive property to multiply \( 2 \) with both \( a \) and \( 5 \). 2. **Associative Property**: \[ 2a + 10 - 4 = 2a + (10 - 4) = 2a + 6 \] Here, the associative property is used to regroup the terms \( 10 \) and \( -4 \) so they can be combined. **Used Properties**: - **Distributive Property** - **Associative Property** The **commutative property** is **not** used in this particular simplification.