Match Equivalent Expressions: (a+g)x+3 and Its Related Forms

Join expressions of equal value

1. $(a+g)x+3$

2. $(x+3)(a+g)$

3. $(a-g)x-3$

   a.$xa+xg+3a+3g$

   b.$ax+gx+3$

   c.$ax-gx-3$

To solve this problem, we'll follow these steps:

• Step 1: Expand each original expression using the distributive property.
• Step 2: Compare each expansion with the given rearranged expressions to find the correct match.

Step 1: Expand each original expression.
- For Expression 1: $(a+g)x+3$ expands to $ax + gx + 3$.
- For Expression 2: $(x+3)(a+g)$ expands to $xa + xg + 3a + 3g$.
- For Expression 3: $(a-g)x-3$ expands to $ax - gx - 3$.

Step 2: Match each expanded expression to the provided options:
- Expression 1: $ax + gx + 3$ matches with option b.
- Expression 2: $xa + xg + 3a + 3g$ matches with option a.
- Expression 3: $ax - gx - 3$ matches with option c.

Therefore, the correct mapping of expressions is:
1-b, 2-a, 3-c.