Question

Can someone please explain Question 8, and how to do it? Thank you!!:)

Answer 1

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