- The Binomial Theorem: A general Formula for expanding a binomial.
- Book Definition: For every positive integer n,
, where P0,P1,Pn, etc are the numbers in the nth row of Pascals Triangles.
- Simple Definition: Every time there is a positive integer n, then use the equation to find the numbers in the nth row of Pascals Triangles.
- Degree of a monomial: This when one varable is the exponent of the variable.
- Degree of a Polynomial: This is the greatest degree among its monomial.
For an example:
- Define expansion(In binomial expansion): To Expand the Power of a binomal, mutiply as needed, then write the polunomial in standard form
Simple Defination: Expansion is the expand of the first binomial in two and then continue to mutiply as needed, then when you get the polynômial, you write it in standard form.
How to: Binomial Expansion Using Pascal’s Triangle
Grade 10; Dee Senaga, Grade 10; Ryko Stylez, Grade 10; Kevin Hubbard
Expanding A Binomial
Vocabulary
Who is Blaise Pascal?
Note:
Pink Numbers Increase
Blue Numbers Decrease
Orange Numbers are Coefficients
- Blaise Pascal is a French Mathematician
- Born on June, 19, 1623 in Clermont Ferrand, French
- Died on August 19, 1662 in Paris
- He was a inventor, Philosopher, Theologian
- He invented The Pascaline, an early calculator, and further validated Evangelista Torricelli's theory concerning the cause of barometrical variations.
- He was named after the Pascal's Triangle
Expand the Binomial by the exponet (2x-3)^4
2x^4-3^0+2x^3-3^1+2x^2-3^2+2x^1-3^3+2x^0-3^4
Now use Pascals Triangle to find your coefficients
Then add the Coefficients to the thing
1*2x^4-3^0+4*2x^3-3^1+6*2x^2-3^2+4*2x^1-3^3+1*2x^0-3^4
Video Example
The Purpose of Binomials Expansion
There are many reasons for using Binomials Expanision:
- Mathematical purpose: To expand and/or mutiply out the power of a binomial in general. Also you can use a pattern of coefficients and the patterns of the Bionomial theorm to write the expansions.
- Real life application Purpose: There are a lot of areas where the application of binomial theorem is used in real life, like computing. In the computing areas, binomial theorem has been very useful such as in distribution of IP addresses. With binomial theorem, the automatic distribution of IP addresses is not only possible but also the distribution of virtual IP addresses. This Therorem has been also used in the architeculture industry in the design of infrastructures.