(a + b + c)² Identity Model

Nine colour-coded tiles fill one square of side (a + b + c), showing every term of (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca as a piece students can hold.

How it works

1. Place the three squares a², b² and c² along the diagonal of the tray
2. Fill the gaps with the six red rectangles: two each of ab, bc and ca
3. The nine pieces fill the (a + b + c) square exactly

What students learn

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• Each term of the identity is an area
• How this identity grows from (a + b)²

Try these activities

1. Check the areas with a = 3, b = 5, c = 7 cm: the total should be 225 cm²
2. Group the pieces to show (a + b)² inside the larger square
3. Use the identity to expand (x + 2y + 3)²

Curriculum fit

In the box

• MDF tray 17 x 17 cm (a = 3, b = 5, c = 7 cm)
• Yellow a², blue b², green c² and six red rectangles
• Step-by-step manual

Pairs well with

(a + b)² Identity ModelMATH-114(a + b)³ Cube ModelMATH-118