Graphing
Calculator
Math
Worksheets
Scientific
Calculator
Chart
Maker


A+    A−    B  
Home
Graphing Calc
Algebra
Fun Games
Geometry
Interactive
Trigonometry
Scientific Calc
Home
Graphing Calc
Algebra
Fun Games
Geometry
Interactive
Trigonometry
Scientific Calc

Binomial Theorem

Method to expand polynomials

The binomial theorem states a formula for expressing the powers of sums. The most succinct version of this formula is shown immediately below.
picture of binomial theorem as infinite series
Isaac Newton wrote a generalized form of the Binomial Theorem. However, for quite some time Pascal's Triangle had been well known as a way to expand binomials (Ironically enough, Pascal of the 17th century was not the first person to know about Pascal's triangle)

A closer look at the Binomial Theorem



The easiest way to understand the binomial theorem is to first just look at the pattern of polynomial expansions below.
  • (x+y)² =x²+2xy + y²
  • (x+y)3 = x3 + 3x2Y+ 3xY2 + y3
  • (x+y)4 =x4+ 4x3Y +6x2Y2 + 4XY3 + Y4

Binomial Theorem Formula

The generalized formula for the pattern above is known as the binomial theorem generalized example of biomial theorem

Practice Problems on the Binomial Theorem



Practice problem 1) Use the formula for the binomial theorem to determine the fourth term in the expansion (y − 1)7
Answer
Practice Problem 2) Make use of the binomial theorem formula to determine the eleventh term in the expansion (2a − 2)12
Answer
Practice Problem 3) Use the binomial theorem formula to determine the fourth term in the expansion
Answer