Which of the following is the third term of the expansion (a + b)n?
C(n, 2)a(n-2) - b2
C(n, 3)a(n-3) - b
C(n, 2)a2 - b(n - 2)
Solution:
Binomial expansion of (x + y)n by using the binomial theorem is as follows,
(x + y)n = nC0 xn + nC1 xn-1 y + nC2 xn-2 y + ….. + nCr xn-r yr + …. + nCn yn
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series.
The binomial theorem states the principle for expanding the algebraic expression (x + y)n and expresses it as a sum of the terms involving individual exponents of variables x and y.
Each term in a binomial expansion is associated with a numeric value which is called coefficient.
According to the binomial expansion for (x + y)n, the formula for tth term is nCr (x)r (y)n - r, where r = t - 1.
Therefore, the third term in the expansion of (a + b)n = C(n, 2)a2 - b(n - 2).
Which of the following is the third term of the expansion (a + b)n?
Summary:
The third term in the expansion of (a + b)n = C(n, 2)a2 - b(n - 2).
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