Question

how to solve (2a+b)3-(2a-b)3

Answer 1

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Answer 2

(2a+b)³ - (2a-b)³ = 2b³ + 24a²b  

Given:

(2a+b)³ - (2a-b)³    

To find:

Solve given expression

Solution:

Formula used:

(a + b)³ = a³ + b³ + 3a²b + 3ab²

(a - b)³ = a³ - b³ - 3a²b + 3ab²    

Given (2a+b)³ - (2a-b)³      

By using the above formula,

=> (2a)³ + (b)³ + 3(2a)²(b) + 3(2a)(b)² - [ (2a)³ - (b)³ - 3(2a)²(b) + 3(2a)(b)² ]  

=> 8a³ + b³ + 12a²b + 6ab² - [ 8a³ - b³ - 12a²b + 6ab² ]    

=> 8a³ + b³ + 12a²b + 6ab² - 8a³ + b³ + 12a²b - 6ab² ]      

=>  b³ + 12a²b + b³ + 12a²b  

=> 2b³ + 24a²b            

Therefore,

(2a+b)³ - (2a-b)³ = 2b³ + 24a²b

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