Question

simplify (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b)

Answer 1

Hey mate!

Answer:
As given that,
=(2a+b)^3-(2a-b)^3-6b (2a+b)(2a-b)
remaining in the pic.....

hope it helps!

Answer 2

(2a + b)³- (2a - b)³- 6b(2a + b)(2a - b)

Expand (2a + b)³ and (2a - b)³ using pascal triangle:

= (8a³ + 12a²b + 6ab² + b³) - (8a³ - 12a²b + 6ab² - b³) - 6b(2a + b)(2a - b)

Expand (2a + b)(2a - b) using algebraic identify (a + b)(a - b) = a² - b²:

= (8a³ + 12a²b + 6ab² + b³) - (8a³ - 12a²b + 6ab² - b³) - 6b(4a² - b²)

Remove brackets:

= 8a³ + 12a²b + 6ab² + b³ - 8a³ + 12a²b - 6ab² + b³ - 24a²b + 6b³

Combine like terms:

=  8b³

Answer:  8b³