# Binomial Theorem Worksheets

What is the Binomial Theorem? A binomial theorem is an algebraic approach used to expand the binomial expression. It shows us how the algebraic will look when a binomial is multiplied by itself. For instance, consider the algebraic expression (4x + y)7. It will take a lot of time to multiply this algebraic expression seven times. Instead of doing that, we employ a binomial theorem that can conveniently give us the result of multiplying this expression seven times. The binomial theorem is the shortcut for getting results of the expansion of algebraic expression. The binomial theorem says that it is possible to expand (x + y)n into mathematical expression in the form of axbyc, where b and c represent the non-negative integer with b + c = n. In this expression, the coefficient 'a' represents the positive integers that depend on the values of b and n. In case we have zero as an exponent, we would omit that power form the algebraic expression. For example, 4x2y0, we will remove y from the expression; the expression will become 3x2.

• ### Basic Lesson

Guides students solving equations that involve Binomial Theorems. Demonstrates answer checking. Most of the syntax used in this theorem should look familiar. The notation is just another way of writing a combination such as n C k(read "n choose k").

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of Binomial Theorems.

• ### Independent Practice 2

Students find the Binomial Theorems in assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of Binomial Theorems.

• ### Skill Quiz

This tests the students ability to evaluate Binomial Theorems.

• ### Answer Key

Answers for math worksheets, quiz, homework, and lessons.

#### Question

Why do you rarely find mathematicians spending much time at the beach?

Answer: Because they have sine and cosine to get a tan and don't really need the sun.