Download Alg II 5-7 The Binomial Theorem

Alg II 5­7 The Binomial Theorem ­ End.notebook
November 04, 2016
5-7 The Binomial Theorem
To expand the power of a binomial, first multiply as needed. Then write the polynomial in standard form.
(a + b)3 a binomial to a power
(a + b)(a + b)(a + b) expand the expression
a3 + 3a2b + 3ab2 + b3
then FOIL and write in standard form.
Consider the expansion of (a + b)n for the first few values of n:
The "coefficients only" column matches the numbers in Pascal's Triangle. Pascal's Triangle is a triangular array of numbers in which the first and last number of each row is 1. Each of the other numbers in the row is the sum of the two numbers above it.
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Alg II 5­7 The Binomial Theorem ­ End.notebook
Ex. 1
November 04, 2016
Expand each binomial. Use Pascal's Triangle.
A.
(a + b)6
B.
(a + b)8
Binomial Theorem
The Binomial Theorem gives a general formula for expanding a binomial.
When you use the Binomial Theorem to expand (x − 2)4, a = x and b = −2. To expand a binomial such as (3x − 2)5, a = 3x so remember that a = (3x)4 not 3x4.
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Alg II 5­7 The Binomial Theorem ­ End.notebook
Ex. 2
Expand each binomial. Use Pascal's Triangle.
A.
(3x − 2)5
B.
(2x − y)7
Ex. 3
November 04, 2016
Find the specified term of each binomial expansion.
A.
Fourth term of (x + 2)5
B.
Third term of (3x − 1)5
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Alg II 5­7 The Binomial Theorem ­ End.notebook
Ex. 4
November 04, 2016
State the number of terms in each expansion and give the first two terms.
A.
(b + 4)7
B.
(2m − 3n)9
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