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What is the x^12 term in the expansion of (2 + x)^24

What is the x^12 term in the expansion of (2 + x)^24

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Answer #1

In the expression of (a + x)^n, the coefficient of second term is nC1, of the third term is nC2, of he fourth term is nC3 and so on. The suffix in each term being one less than the number of the term to which it applies; hence nCr is the coefficient of the (r+1)th term. This is called the General Term, because by giving different numerical values to r any of the coefficients may be found. Also, the indices of a and x in the (r + 1)th term are expressable in terms of r.

Thus, General term of the expansion (a + x)^n is dented as

Tr+1 = nCr a^(n-r) x^r

Put r = 12 for x^12

13th term it means

T13 = 24C12 * 2^12 * x^12

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