Question

please answer this question with full process
(a+b)^3-(a-b)^3

Answer 1

Sol : Let A = ( a + b ) and B = ( a - b ).

Using identity , A³ - B³ = ( A - B ) ( A² + B² + AB )

By substituting the value of A and B in above identity ,

( a + b )³ - ( a - b )³ = { ( a + b ) - ( a - b ) } { ( a + b )² + ( a - b )² + ( a + b ) ( a - b )}


= { a + b - a + b } { a² + b² + 2 ab + a² + b² - 2 ab + a² - ab + ab - b² }

= ( 2 b ) ( 3 a² + 2 b² + 3 ab - 3 ab - b² )

= ( 2 b ) ( 3 a² + b² ) 
     
                            __________________________________

Answer 2

x^3-y^3=(x-y)^3+3xy(x-y)
so,
(2b)^3+3(a^2-b^2)(2b)
8b^3+6b*a^2-6b^3
2b^3+6b*a^2