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Binomial Expansion
Binomial Expansion
Vocabulary
Expansion/Expand: Means to multiply the binomial/polynomial to the end and then writing it in standard form.
Pascal's Triangle: Is named for the mathematician Blaise Pascal (1623-1662)
Binomial Theorem: Gives a general formula for expanding a binomial.
Coefficient: The number multiplied with a variable.
By Amanda Grade 9 and Vlad GRade 10
Binomial: an equation or an expression that contains two variables
Degree: How many times the number or polynomial multiplies with itself.
The trick to expanding binomials faster.
(a+b)^12
Pascal's Triangle
Using Pascal's triangle will help you expand binomials faster than traditional multiplying binomials together.
1. Blaise Pascal was born in France in 1623.
2. He was a mathematician, physicist, inventor, and writer and Christian philosopher.
3.He was a child prodigy who was educated by his father, a tax collector in Rouen.
4. The “Pascal’s Triangle” was named after him.
List of polynomials
Solution
a^12+12 a^11 b+66 a^10 b^2+220 a^9 b^3+495 a^8 b^4+792 a^7 b^5+924 a^6 b^6+792 a^5 b^7+495 a^4 b^8+220 a^3 b^9+66 a^2 b^10+12 a b^11+b^12
This is the list of the polynomials that is the answer without the coefficients. The exponents must add up the the original degree that was originally getting expanded.
a^12+12
a^11 b
a^10b^2
a^9b^3
a^8b^4
a^7 b^5
a^6 b^6
a^5 b^7
a^4 b^8
a^3 b^9
a^2b^10
a^1b^11
b^12