Proof for the equations are given below.
Step-by-step explanation:
- Step 1: The diagram is made up of 1 square and 4 rectangles, and the whole figure is a square. So the area of the larger square (figure) must be equal to the sum of the areas of the 4 rectangles and 1 square. Find the area of the figure or the larger square.
Area of a square = (side length)²
Here, the length of the side of the larger square = a + b
⇒ Area of the square = (a + b)²
- Step 2: Find the sum of the areas of the 1 square and 4 rectangles.
Here, the side of the square = a - b
⇒ Area of the square (in the center) = (a - b)²
Area of a rectangle = length × width
Here, length = a and width = b
⇒ Area of the 4 rectangles = 4 × a × b = 4ab
∴ Sum of the areas = (a - b)² + 4ab
Now, both these areas are the same.
⇒ (a - b)² + 4ab = (a + b)²
- Step 3: Expand the above equation.
Left Hand Side = (a - b)² + 4ab = a² - 2ab + b² + 4ab = a² + 2ab + b²
= (a + b)²
= Right Hand Side of the equation
