5.7 The Binomial Theorem Name: Objectives: Students will be able

5.7 The Binomial Theorem
Name: ___________________
Objectives: Students will be able to expand a binomial using
Pascal's Triangle. Students will be able to use the Binomial
Theorem.
There are numerical patterns in the expansion of powers of
binomials. Let's examine the expansion of (x + y)n.
(x + y)0 =
(x + y)1 =
(x + y)2 =
(x + y)3 =
(x + y)4 =
(x + y)5 =
1x0y0
1x1y0 + 1x0y1
1x2y0 + 2x1y1 + 1x0y2
1x3y0 + 3x2y1 + 3x1y2 + 1x0y3
0 4
1x4y0 + 4x3y1 + 6x2y2 + 4x1y3 + 1x y
0 5
1 4
1x5y0 + 5x4y1 + 10x3y2 + 10x2y3 + 5x y + 1x y
Dec 19­1:49 PM
Let's look at the coefficients only.
Dec 19­1:49 PM
1
If just the coefficients are extracted and arranged in a
triangular array, they form a pattern called _______________.
1
1
1
1
2
1
A Bit of History
Blaise Pascal
(1623-1662)
Blaise Pascal was a ___________________, __________,
_________, _________ and ________________. He invented
the _________________. His greatest influences have been in
the fields of _________________ and _________________.
Dec 19­1:50 PM
The Binomial Theorem gives a general formula for expanding a
binomial using Pascal's Triangle. We'll look at some examples
below.
Expand each binomial using the Binomial Theorem.
2.) (a + b)8
1.) (x + y)6
Dec 19­1:51 PM
2
4.) (4a + 3b)7
3.) (2x - y)6
Dec 19­1:54 PM
5.7 ICE
Name: ________________
Expand each binomial using the Binomial Theorem.
1.) (x - 5)4
2.) (5a + 2b)3
Dec 19­1:54 PM
3
Jan 2­9:41 AM
4