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```6-2
Multiplying Polynomials
Objectives
Multiply polynomials.
Use binomial expansion to expand
binomial expressions that are raised to
positive integer powers.
To multiply a polynomial by a monomial, use
the Distributive Property and the Properties
of Exponents.
Holt Algebra 2
6-2
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
B. fg(f4 + 2f3g – 3f2g2 + fg3)
fg(f4 + 2f3g – 3f2g2 + fg3)
fg  f4 + fg  2f3g – fg  3f2g2 + fg  fg3
f5g + 2f4g2 – 3f3g3 + f2g4
Holt Algebra 2
6-2
Multiplying Polynomials
Check It Out! Example 1
Find each product.
a. 3cd2(4c2d – 6cd + 14cd2)
b. x2y(6y3 + y2 – 28y + 30)
Holt Algebra 2
6-2
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.
Keep in mind that if one polynomial has m terms
and the other has n terms, then the product has
mn terms before it is simplified.
Holt Algebra 2
6-2
Multiplying Polynomials
Example 2A: Multiplying Polynomials
Find the product.
(a – 3)(2 – 5a + a2)
Method 1 Multiply horizontally.
(a – 3)(a2 – 5a + 2)
a(a2) + a(–5a) + a(2) – 3(a2) – 3(–5a) –3(2)
a3 – 5a2 + 2a – 3a2 + 15a – 6
a3 – 8a2 + 17a – 6
Holt Algebra 2
6-2
Multiplying Polynomials
Example 2A: Multiplying Polynomials
Find the product.
(a – 3)(2 – 5a + a2)
Method 2 Multiply vertically.
a2 – 5a + 2
a–3
– 3a2 + 15a – 6
a3 – 5a2 + 2a
a3 – 8a2 + 17a – 6
Holt Algebra 2
6-2
Multiplying Polynomials
Check It Out! Example 2a
Find the product.
(3b – 2c)(3b2 – bc – 2c2)
Holt Algebra 2
Multiply horizontally.
6-2
Multiplying Polynomials
Check It Out! Example 2b
Find the product.
Multiply vertically
(x2 – 4x + 1)(x2 + 5x – 2)
Holt Algebra 2
6-2
Multiplying Polynomials
Find the product.
Holt Algebra 2
(a + 2b)3
6-2
Multiplying Polynomials
Find the product.
Holt Algebra 2
(x + 4)4
6-2
Multiplying Polynomials
Find the product.
Holt Algebra 2
(2x – 1)3
6-2
Multiplying Polynomials
Lesson Quiz
Find each product.
1. 5jk(k – 2j) 5jk2 – 10j2k
2. (2a3 – a + 3)(a2 + 3a – 5)
2a5 + 6a4 – 11a3 + 14a – 15
3.
(3a – b)3
Holt Algebra 2
27a3 – 27a2b + 9ab2 – b3
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