(3) (a + b)3 – a3 – b3
Solution
The given expression is (3) (a + b)³ – a³ – b³.
Let's simplify it step by step:
Step 1: Distribute the 3 to (a + b)³ This gives us 3(a + b)³ – a³ – b³.
Step 2: Expand (a + b)³ using the binomial theorem which states (a + b)³ = a³ + 3a²b + 3ab² + b³. This gives us 3(a³ + 3a²b + 3ab² + b³) – a³ – b³.
Step 3: Distribute the 3 in the expanded form. This gives us 3a³ + 9a²b + 9ab² + 3b³ – a³ – b³.
Step 4: Combine like terms. This gives us 2a³ + 9a²b + 9ab² + 2b³.
So, (3) (a + b)³ – a³ – b³ simplifies to 2a³ + 9a²b + 9ab² + 2b³.
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