 # Binomial Theorem Worksheet

The Binomial theorem being a part of the elementary algebra, explains the powers of a binomial as algebraic expressions. As we know that a binomial is a type of polynomial with two terms. What happens if the binomial is multiplied by itself many times. As the power of the binomial term is increased, the process becomes tedious and more lengthy. When we multiply the binomial, some pattern should be developed. The pattern obtained can be summed using the binomial theorem. The binomial theorem formula is given as follows:

$$(a+b)^{n} =\sum_{k=0}^{n}\begin{pmatrix} n\\ k \end{pmatrix}a^{n-k}b^{k}$$

In other words, the binomial theorem is the process of expanding the given binomial expression, which is raised to any finite power. The theorem states that, for any positive integer, say “n”, the nth power of the sum of the terms “a” and “b”, can be expressed as the sum of “n+1” terms of the form. The binomial theorem is applicable if the binomial expression has two different terms. For example, (a+b)4, (x+y)5, and so on. In the binomial expansion, frequently we can expect questions like finding the middle term, or general term or the particular term. The binomial theorem has huge applications in the various concepts of mathematics, such as finding the particular digit of a number, finding remainder and so on. The generalization of this theorem is used to solve and prove many problems in calculus, combinatorics, algebra, and so on.

Here we have provided a worksheet for problems based on the binomial theorem as it would be helpful for students who wish to know more about different aspects of this theorem.

### Worksheet on Binomial Theorem

Expand the following expressions using binomial theorem:

 (2x+4y)3 (4x+3y)6 (8x+4y)2 (5x+2y)3 (x+3y)2 (2a+b)5 Determine the 5th term of (5x+b2)7. Calculate the last term of (6x+9)5. Find the third term of (7x+2)5. Determine the 3rd term of (4x+2b2)6.

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