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Solve the following with the method:
Method - (a + b)³=a³+3×a²×b+3×a×b²+b³
1. 50³
2. 1002³
3. 678³
4. 901³
5. 5890³
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.
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Answer:
Answer is 1,125000
Answer 2 1006012008
Answer. 3 311665752
Answer. 4. 731432701
Answer 5. 204336469000
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1
What is the formula for a³-b³?
a³-b³=(a-b)(a²+ab+b²)
Proof
We know
(a-b)³=a³-b³-3a²b+3b²a
a³-b³=(a-b)³+3a²b-3b²a
a³-b³=(a-b)³+3ab(a-b)
Taking (a-b) common
a³-b³=(a-b)((a-b)²+3ab)
Using indentity (a-b)²=a²+b²-2ab
a³-b³=(a-b)(a²+b²-2ab+3ab)
Therefore a³-b³=(a-b)(a²+b²+ab)
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