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

Question

Join expressions of equal value

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

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

  3. (ag)x3 (a-g)x-3

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

    b.ax+gx+3 ax+gx+3

    c.axgx3 ax-gx-3

Video Solution

Step-by-Step Solution

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 (a+g)x+3 expands to ax+gx+3 ax + gx + 3 .
- For Expression 2: (x+3)(a+g) (x+3)(a+g) expands to xa+xg+3a+3g xa + xg + 3a + 3g .
- For Expression 3: (ag)x3 (a-g)x-3 expands to axgx3 ax - gx - 3 .

Step 2: Match each expanded expression to the provided options:
- Expression 1: ax+gx+3 ax + gx + 3 matches with option b.
- Expression 2: xa+xg+3a+3g xa + xg + 3a + 3g matches with option a.
- Expression 3: axgx3 ax - gx - 3 matches with option c.

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

Answer

1-b, 2-a, 3-c