Question

GEOMETRICAL PROOFS of (a+b)² , (a-b)² and ( a²-b²)​

Answer 1

Answer:

GEOMETRICAL PROOF OF (a+b)²:-

• Take a square and divide it into two different parts vertically. The lengths of them are a and b respectively.
• Similarly, divide the square horizontally with same lengths. So, the widths of them are also a and b respectively.
• The length and width of the square are same and the length of its each side is a+b. Therefore, the area of the square is (a+b) × (a+b) = (a+b)² geometrically.

GEOMETRICAL PROOF OF (a-b)²:-

• Draw a square ACDF with AC = a units.
• Cut AB=b units so that BC=(a−b) unts.
• Complete the squares and rectangle as shown in the diagram.
• Area of yellow square IDEO= Area of square ACDF − Area of rectangle GOFE − Area of rectangle BCIO − Area of red square ABOG.

Therefore, (a−b)² = a² − b(a−b) − b(a−b)−b²

= a² - ab + b² - ab + b² - b²

= a² - 2ab + b²

GEOMETRICAL PROOF OF a² - b²:-

• Take a square, whose length of each side is a units. Therefore, the area of the square is a².
• Draw a small square with the side of b units at any corner of the square. So, the area of small square is b².
• Now, subtract the square, whose area is b² from the square, whose area is a² It forms a new geometric shape and its area is equal to a² - b²

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