Download 3. - My CCSD

3-2
Multiplying Polynomials
Warm Up
Multiply.
1. x(x3) x4
2. 3x2(x5) 3x7
3. 2(5x3) 10x3
4. x(6x2) 6x3
5. xy(7x2)
7x3y
6. 3y2(–3y)
–9y3
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
Objectives
Multiply polynomials.
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
Example 1: Multiplying a Monomial and a Polynomial
Find each product.
A. 4y2(y2 + 3)
4y2(y2 + 3)
4y2  y2 + 4y2  3
4y4 + 12y2
Distribute.
Multiply.
B. fg(f4 + 2f3g – 3f2g2 + fg3)
fg(f4 + 2f3g – 3f2g2 + fg3)
fg  f4 + fg  2f3g – fg  3f2g2 + fg  fg3 Distribute.
f5g + 2f4g2 – 3f3g3 + f2g4
Multiply.
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
To multiply any two polynomials, use the
Distributive Property and multiply each term in
the second polynomial by each term in the first.
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
Example 2: Multiplying Polynomials
Find the product.
(a – 3)(2 – 5a + a2)
(a – 3)(a2 – 5a + 2) Write polynomials in standard form.
Distribute a and then –3.
a(a2) + a(–5a) + a(2) – 3(a2) – 3(–5a) –3(2)
a3 – 5a2 + 2a – 3a2 + 15a – 6 Multiply. Add exponents.
a3 – 8a2 + 17a – 6
Holt McDougal Algebra 2
Combine like terms.
3-2
Multiplying Polynomials
Example 3: Multiplying Polynomials
Find the product.
(y2 – 7y + 5)(y2 – y – 3)
Multiply each term of one polynomial by each term of
the other. Use a table to organize the products.
y2
–y
–3
The top left corner is the first
2
4
3
2
y
y
–y –3y
term in the product. Combine
terms along diagonals to get
–7y –7y3 7y2 21y
the middle terms. The bottom
right corner is the last term in
5
2
5y
–5y –15 the product.
y4 + (–7y3 – y3 ) + (5y2 + 7y2 – 3y2) + (–5y + 21y) – 15
y4 – 8y3 + 9y2 + 16y – 15
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
CLASSWORK
Worksheet
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
CLASSWORK
Worksheet
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
Objectives
Use binomial expansion to expand
binomial expressions that are raised to
positive integer powers.
Holt McDougal Algebra 2
3-2
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
3-2
Multiplying Polynomials
Example 1: Using Pascal’s Triangle to Expand
Binomial Expressions
Expand each expression.
A. (k – 5)3
1331
Identify the coefficients for n = 3, or row 3.
1(k)3 + 3(k)2(–5) + 3(k)(–5)2 + 1(–5)3
k3 – 15k2 + 75k – 125
B. (3x + 1)4
14641
Identify the coefficients for n = 4, or row 4.
1(3x)4 + 4(3x)3(1) + 6(3x)2(1)2 + 4(3x)(1)3 + 1(1)4
81x4 + 108x3 + 54x2 + 12x + 1
Holt McDougal Algebra 2
3-2
Multiplying Polynomials
CLASSWORK
Worksheet
Holt McDougal Algebra 2