Question

show that (a+b)^2-(a-b)^2=4ab

Answer 1

( a + b )² - ( a - b )² = 4ab

LHS = ( a + b)² - ( a - b )²

=> ( a)² + (b)² + 2ab - { ( a)² + (b)² - 2ab ) }

=> a² + b² + 2ab - ( a² + b² - 2ab )

=> a² + b² + 2ab - a² - b² + 2ab

=> a² - a² + b² - b² + 2ab + 2ab

=> 2ab + 2ab

=> 4ab

Hence,

LHS = RHS = 4ab

Answer 2

(a+b)²=a²+b²+2ab................................................(1)

and

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

subtracting equation (2) from (1) we get..

(a+B)²-(a-B)2 =4ab

hope you will get it