Question

simplify (2a+b) ³-(2a-b)³
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Answer 1

FINAL ANSWER:

24 a²b + 2 b³

GIVEN:

(2a+b) ³-(2a-b)³

TO FIND:

(2a+b) ³- (2a-b)³

FORMULA USED:

(a-b)³=a³-3a²b+3ab²-b³

And,

(a+b)³=a³+3a²b+3ab²+b³

SOLUTION:

(a-b)³=a³-3a²b+3ab²-b³

(a+b)³=a³+3a²b+3ab²+b³

Now,

(a+b)³ - (a-b)³ = {a³+3a²b+3ab²+b³} - {a³-3a²b+3ab²-b³}  

= 6a²b+ 2b³ ————- equation (1)

Similarly, (2a+b)³ - (2a-b)³

here a = 2a & b = b

Substitute these values in equation (1)

⇒ 6 (4a²b) + 2 b³ = 24 a²b + 2 b³

24 a²b + 2 b³

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