The sum of the coefficient of (1+x/3 + 2y/3 ) to the power 12 is....
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Solution. We found the binomial coefficients to be 1 5 10 10 5 1. The difference with (a − b) is that the signs of the terms will alternate:
(a − b)5 = a5 − 5a4b + 10a3b2 − 10a2b3 + 5ab4 − b5.
For, a − b = a + (−b), therefore each term will have the form
a5 − k(−b)k.
When k is even, (−b)k will be positive. But when k is odd, (−b)k will be negative.
Each odd power of b will have a minus sign.
(a − b)5 = a5 − 5a4b + 10a3b2 − 10a2b3 + 5ab4 − b5.
For, a − b = a + (−b), therefore each term will have the form
a5 − k(−b)k.
When k is even, (−b)k will be positive. But when k is odd, (−b)k will be negative.
Each odd power of b will have a minus sign.
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