The following formula allows one to find the powers of a binomial. It is known as the binomial theorem.

Observe that:

The number of terms is n + 1.

The coefficients are combinatorial numbers corresponding to the nth row of Pascal's triangle.

In the development of the binomial, the exponents of a are decreasing, one by one, from n to zero; and the exponents of b are increasing, one by one, from zero to n, therefore, the sum of the exponents of a and b in each term is equal to n.

In the case that one of the terms of the binomial is negative, alternate the positive and negative signs.








Calculation of the Term which Occupies the Place k


1. Find the fifth term of the development .

2.Find the fourth term of the development is:

3.Find the eighth term of the development

4.Find the fifth term of the development .

5.Find the independent term of the development .

The exponent of a with the independent term is 0, therefore, take only the literal part and equal it to a0.

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