holt algebra 2 6-2 multiplying polynomials multiply polynomials. use binomial expansion to expand...
TRANSCRIPT
Holt Algebra 2
6-2 Multiplying Polynomials
Multiply polynomials.
Use binomial expansion to expand binomial expressions that are raised to positive integer powers.
Objectives
To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.
Holt Algebra 2
6-2 Multiplying Polynomials
Find each product.
Example 1: Multiplying a Monomial and a Polynomial
A. 4y2(y2 + 3)
B. fg(f4 + 2f3g – 3f2g2 + fg3)
4y2 y2 + 4y2 3
4y2(y2 + 3)
4y4 + 12y2
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
Find the product.
Example 2A: Multiplying Polynomials
(a – 3)(2 – 5a + a2)
a(a2) + a(–5a) + a(2) – 3(a2) – 3(–5a) –3(2)
Method 1 Multiply horizontally.
a3 – 5a2 + 2a – 3a2 + 15a – 6
a3 – 8a2 + 17a – 6
(a – 3)(a2 – 5a + 2)
Holt Algebra 2
6-2 Multiplying Polynomials
(a – 3)(2 – 5a + a2)
Find the product.
Example 2A: Multiplying Polynomials
Method 2 Multiply vertically.
a2 – 5a + 2 a – 3
– 3a2 + 15a – 6a3 – 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)
Multiply horizontally.
Holt Algebra 2
6-2 Multiplying Polynomials
(x2 – 4x + 1)(x2 + 5x – 2)
Find the product.Check It Out! Example 2b
Multiply vertically
Holt Algebra 2
6-2 Multiplying PolynomialsFind the product. (a + 2b)3
Holt Algebra 2
6-2 Multiplying PolynomialsFind the product. (x + 4)4
Holt Algebra 2
6-2 Multiplying Polynomials
Find the product. (2x – 1)3
Holt Algebra 2
6-2 Multiplying Polynomials
Lesson Quiz
2. (2a3 – a + 3)(a2 + 3a – 5)
5jk2 – 10j2k1. 5jk(k – 2j)
2a5 + 6a4 – 11a3 + 14a – 15
Find each product.
3. (3a – b)3
27a3 – 27a2b + 9ab2 – b3