Transcript Holt McDougal Algebra 2

Multiplying Polynomials
• How do we multiply polynomials?
•How do we use binomial expansion to
expand binomial expressions that are
raised to positive integer powers?
Holt McDougal Algebra 2
Multiplying Polynomials
Notice the coefficients of the variables in the final
product of (a + b)3. These coefficients are the numbers
from the third row of Pascal's triangle.
Each row of Pascal’s triangle gives the coefficients of the
corresponding binomial expansion. The pattern in the table
can be extended to apply to the expansion of any binomial
of the form (a + b)n, where n is a whole number.
Holt McDougal Algebra 2
Multiplying Polynomials
This information is formalized by the Binomial
Theorem, which you will study further in Chapter 11.
Holt McDougal Algebra 2
Multiplying Polynomials
Using Pascal’s Triangle to Expand Binomial
Expressions
Expand each expression.
1. (k – 5)3
Identify the coefficients for n = 3, or row 3.
1331
[1(k)3(–5)0] + [3(k)2(–5)1] + [3(k)1(–5)2] + [1(k)0(–5)3]
k  1 5 k  7 5 k  12 5
2
3
2. (6m – 8)3
Identify the coefficients for n = 3, or row 3.
1331
[1(6m)3(–8)0] + [3(6m)2(–8)1] + [3(6m)1(–8)2] + [1(6m)0(–8)3]
216m  864m  1152 m  512
3
Holt McDougal Algebra 2
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Multiplying Polynomials
Using Pascal’s Triangle to Expand Binomial
Expressions
Expand each expression.
3. (x + 2)3
1 3 3 1 Identify the coefficients for n = 3, or row 3.
[1(x)3(2)0] + [3(x)2(2)1] + [3(x)1(2)2] + [1(x)0(2)3]
2
3
x  6 x  12 x  8
4. (x – 4)5
1 5 10 10 5 1
Identify the coefficients for n = 5, or row 5.
[1(x)5(–4)0] + [5(x)4(–4)1] + [10(x)3(–4)2] + [10(x)2(–4)3]
+ [5(x)1(–4)4] + [1(x)0(–4)5]
x  20 x  160 x  640 x  1280 x  1024
5
4
Holt McDougal Algebra 2
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Multiplying Polynomials
Using Pascal’s Triangle to Expand Binomial
Expressions
Expand the expression.
5. (3x + 1)4
Identify the coefficients for n = 4, or row 4.
14641
[1(3x)4(1)0] + [4(3x)3(1)1] + [6(3x)2(1)2]
+ [4(3x)1(1)3] + [1(3x)0(1)4]
81x  108 x  54 x  12 x  1
4
Holt McDougal Algebra 2
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Multiplying Polynomials
Lesson 3.2 Practice C
Holt McDougal Algebra 2