Creating a working model to demonstrate algebraic identities using cardboard and two holes can be an interesting and visual way to showcase mathematical concepts.

Here’s a simple DIY project for an algebraic identities working model:

**Materials Needed:**

- Cardboard
- Ruler
- Pencil
- Scissors
- String or yarn
- Markers
- Colored paper
- Glue or tape
- Compass
- Brass fasteners (optional)

**Steps to Create the Algebraic Identities Working Model:**

**Step 1: Cut Cardboard:**

- Cut a large piece of cardboard to serve as the base for your working model.

**Step 2: Draw Circles:**

- Use a compass to draw two circles on the cardboard. These will represent the holes.

**Step 3: Cut Holes:**

- Cut out the circles to create the holes in the cardboard.

**Step 4: Label the Circles:**

- Label each hole with a variable, such as ‘a’ and ‘b,’ to represent the algebraic expressions.

**Step 5: Create Flaps:**

- Cut rectangular flaps on the cardboard around each hole, leaving enough space to write or attach the algebraic expressions.

**Step 6: Write or Attach Expressions:**

- Write the algebraic expressions corresponding to each identity on the flaps or attach colored paper with the expressions.

**Step 7: Attach Strings:**

- Cut two pieces of string or yarn, and thread them through the holes. Tie knots on the backside to secure them.

**Step 8: Display and Explain:**

- Set up your working model at the exhibition table.
- Pull the strings through the holes to visually demonstrate the algebraic identities.

**Step 9: Optional – Brass Fasteners:**

- Instead of string, you can use brass fasteners to attach the expressions to the holes, allowing for easy rotation.

**Explanation:**

- During your exhibition, explain each algebraic identity and how pulling the strings or rotating the expressions visually demonstrates the validity of the identities.

This working model provides a tangible representation of algebraic identities, making it an engaging and interactive display for a math project or exhibition. It allows students and visitors to physically manipulate the expressions, enhancing their understanding of algebraic concepts.