Question

12. Show that (a+b)² -(a - b)²
= 4ab.

plz give me right answer ​

Answer 1

solution

a² + 2ab + b² - ( a - b ) ² = 4ab

a² + 2ab + b² - ( a² - 2ab + b² ) = 4ab

a² + 2ab + b² - a² + 2ab - b² = 4ab

2ab + b² + 2ab + b² = 4ab

4ab + b² - b² = 4ab

4ab = 4ab

4ab - 4ab = 0

0 = 0

Answer 2

Explanation:

(a+b)^2= a^2 + 2ab + b^2

(a-b)^2= a^2 - 2ab + b^2

substituting this in place of (a+b)² -(a - b)²:

(a+b)² -(a - b)²

=> (a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)= 0

a^2 + 2ab + b^2 - a^2 + 2ab - b^2=0

a^2 - a^2 + 2ab + 2ab + b^2 - b^2=0

2ab+ 2ab= 4ab .......

HENCE PROVED.....