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(1) (2a + b)3 – (2a – b)3

Question

(1) (2a + b)3 – (2a – b)3

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Solution

Sure, let's solve this step by step:

First, let's expand the cubes:

(1) (2a + b)³ = 8a³ + 12a²b + 6ab² + b³

(2) (2a - b)³ = 8a³ - 12a²b + 6ab² - b³

Now, let's subtract the second equation from the first:

(2a + b)³ - (2a - b)³ = (8a³ + 12a²b + 6ab² + b³) - (8a³ - 12a²b + 6ab² - b³)

This simplifies to:

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

= 24a²b + 2b³

So, (2a + b)³ - (2a - b)³ = 24a²b + 2b³.

This problem has been solved

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3log b​ 2−log b​ 2

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