Question

Identify the property that justifies each step about the answer and the area below. Line 1: b(a+8) line 2: ba+bx7 line 3: ab+7b. line one to line is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 2 to line 3 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property

Answer 1

To identify the properties that justify each step, let us analyze the lines given:

**Line 1:** \( b(a + 8) \)

**Line 2:** \( ba + b \cdot 7 \)

**Line 3:** \( ab + 7b \)

### Transition from Line 1 to Line 2:
The transition from Line 1 to Line 2 can be justified by the **Distributive Property**. The Distributive Property states that for any numbers \( a, b, \) and \( c \):

\[
b(a + c) = ba + bc
\]

In this case, with \( c = 8 \):

\[
b(a + 8) = ba + b \cdot 8
\]

Thus, **Line 1 to Line 2** is justified by the **Distributive Property**.

### Transition from Line 2 to Line 3:
The transition from Line 2 to Line 3 can be justified by the **Commutative Property of Multiplication**. The Commutative Property of Multiplication states that for any numbers \( x \) and \( y \):

\[
xy = yx
\]

Thus, \( b \cdot 7 = 7b \). So, we can rewrite \( ba + b \cdot 7 \) as \( ab + 7b \).

Therefore, **Line 2 to Line 3** is justified by the **Commutative Property of Multiplication**.

### Summary:
1. **Line 1 to Line 2**: Distributive Property
2. **Line 2 to Line 3**: Commutative Property of Multiplication