(2a+b)cube-(2a-b)cube
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Answered by
2
(2a + b)^3 = (2a)^3 + 3 (2a)^2 b + 3 (2a) b^2 + b^3 = 8a^3 + 12 (a^2 b) + 6ab^2 + b^3
(2a - b)^3 = (2a)^3 - 3 (2a)^2 b + 3 (2a) b^2 - b^3 = 8a^3 - 12 (a^2 b) + 6ab^2 - b^3
Then subtracting
= 24 (a^2 b) + 2b^3
(2a - b)^3 = (2a)^3 - 3 (2a)^2 b + 3 (2a) b^2 - b^3 = 8a^3 - 12 (a^2 b) + 6ab^2 - b^3
Then subtracting
= 24 (a^2 b) + 2b^3
Answered by
6
Here's your answer
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( 2a + b )^3 - ( 2a - b )^3
= { ( 2a + b ) - ( 2a - b ) } [ ( 2a + b )^2 + ( 2a + b ) ( 2a - b ) + ( 2a - b )^2 ]
= ( 2a + b - 2a + b ) [ 4a^2 + 4ab + b^2 + 4a^2 - b^2 + 4a^2 - 4ab + b^2 ]
= 2b [ 12a^2 + b^2 ]
= 24a^2b + 4b^3
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