# Which of the following is the third term of the expansion (a + b)^{n}?

C(n, 2)a^{(n-2)} - b^{2}

C(n, 3)a^{(n-3)} - b

C(n, 2)a^{2} - b^{(n - 2)}

**Solution:**

Binomial expansion of (x + y)n by using the binomial theorem is as follows,

(x + y)^{n} = ^{n}C_{0} x^{n} + ^{n}C_{1} x^{n-1} y + ^{n}C_{2} x^{n-2} y + ….. + ^{n}C_{r} x^{n-r} y^{r} + …. + ^{n}C_{n} y^{n}

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 ^{n}C_{r} (x)^{r} (y)^{n - r}, where r = t - 1.

Therefore, the third term in the expansion of (a + b)^{n} = C(n, 2)a^{2} - 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)a^{2} - b^{(n - 2)}.

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