Question

(a-b) whole square = (a+b) whole square - 4ab​

Answer 1

(a-b)² = a² + b² -2ab

(a-b)² = a² + b² - 2ab - 2ab + 2ab

(adding 2ab and -2ab)

(a-b)² = a² + b² +2ab -4ab

(a-b)² = (a+b)² -4ab.

hence proved...

Answer 2

Given:

An Equation ( a - b ) ² = ( a + b )² - 4ab.

To Find:

The proof of the above equation.

Solution:

The given problem can be solved using the formulae of (a+b)² and (a-b)².

1. The given equation is (a + b)² = (a + b)² - 4ab.

2. The expansions of the  (a - b)² and (a + b)² are,

• (a - b)² = a² + b² - 2ab.
• (a + b)² = a² + b² + 2ab.

3. The expansion of (a - b)² can also be written as,

=>  (a - b)² = a² + b² - 2ab,

=>  (a - b)² = a² + b² + 2ab - 2ab - 2ab, ( Adding and subtracting 2ab).

=>  (a - b)² = a² + b² + 2ab - 4ab,

=> (a - b)² = (a + b)² - 4ab ( Since a² + b² + 2ab =  (a + b)²).

Hence proved.

Therefore, the equation (a - b)² = (a + b)² - 4ab is correct and is proved.