Binomial Theorem Keeper 10 Honors Algebra II What Is a Factorial Evaluate the Factorial Evaluate the Factorial Evaluate Evaluate the Factorial Evaluate Evaluate Evaluate ID: 763917
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Binomial Theorem Keeper 10 Honor’s Algebra II
What Is a Factorial?
Evaluate the Factorial
Evaluate the Factorial
Evaluate:
Evaluate the Factorial
Evaluate:
Evaluate:
Evaluate:
The Binomial Coefficient (Combination) Where n is the number of objects from which you can choose and k is the number to be chosen.
Find the Binomial Coefficient
Evaluate
Evaluate
Evaluate
Evaluate
In the binomial expansion theorem, the numbers, variables , & exponents follow a pattern! *Number of terms in your answer = n + 1 *Coefficients follow Pascal's Triangle of Coefficients *Each expansion will begin with "a" and end with "b" & In between them will be "sets" of "ab's" *Exponents will decrease for "a" from left to right and decrease for "b" from right to left *Exponents on each terms add up to the n value
How to set up the binomial expansion theorem: Step 1: Write out Pascal’s Triangle of Coefficients Step 2 : using the exponent, count down from left to right starting with “a” Step 3: Using the exponent, count down from right to left starting with “b” Step 4 : Simplify your terms
Expand the Following
Expand the Following
Expand the Following ***When there is subtraction in the binomial, the signs should alternate!!!
Expand the Following
Example: Find the 3rd term of the polynomial using The Binomial Expansion Theorem.
Example: Find the Coefficient of the 3rd term of the polynomial using The Binomial Expansion Theorem.
Example: Find the 3rd term of the polynomial using The Binomial Expansion Theorem.