(a + b)^1 = a + b
(a + b)^2 = a^2 + 2a^1b^1 + b^2
(a + b)^3 = a^3 + 3a^2b^1 + 3a^1b^2 + b^3
(a + b)^4 = a^4 + 4a^3b^1 + 6a^2b^2 + 4a^1b^3 + b^4
(a + b)^5 = a^5 + 5a^4b^1 + 10a^3b^2 + 10a^2b^3 + 5a^1b^4 + b^5
(a + b)^6 = a^6 + 6a^5b^1 + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6a^1b^5 + b^6
The coefficients in these binomial expansions follow what is called a Pascal's Triangle:
(a + b)^2 = a^2 + 2a^1b^1 + b^2
(a + b)^3 = a^3 + 3a^2b^1 + 3a^1b^2 + b^3
(a + b)^4 = a^4 + 4a^3b^1 + 6a^2b^2 + 4a^1b^3 + b^4
(a + b)^5 = a^5 + 5a^4b^1 + 10a^3b^2 + 10a^2b^3 + 5a^1b^4 + b^5
(a + b)^6 = a^6 + 6a^5b^1 + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6a^1b^5 + b^6
The coefficients in these binomial expansions follow what is called a Pascal's Triangle:
1 1
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1 2 1
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1 3 3 1
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1 4 6 4 1
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1 5 10 10 5 1
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1 6 15 20 15 6 1
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