Perfect-square formula (area model)

Overview

Area model for (a + b)² = a² + 2ab + b².

Explanation

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².
Area: the big square of side a + b splits into a², b², and two ab rectangles.
Do not drop the middle 2ab term when expanding.

How to use

Adjust a and b; four regions’ areas sum to the expanded perfect square.

Knowledge points

• Factoring
• Algebra