Embed Size (px)
Citation preview
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 2
Exponents and Polynomials
Chapter 5
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 3
5.3
Multiplying Polynomials
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 4
5.3 Multiplying Polynomials
Objectives
1. Multiply a monomial and a polynomial.2. Multiply two polynomials.3. Multiply binomials by the FOIL method.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 5
5.3 Multiplying Polynomials
Multiplying a Monomial and a Polynomial
(a) 5x ( 6x + 7 ) 2 4
Distributive property= 5x ( 6x ) 2 4 + 5x ( 7 ) 2
= 30x + 35x 6 2 Multiply monomials.
Example 1 Find each product.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 6
5.3 Multiplying Polynomials
Multiplying a Monomial and a Polynomial
Distributive property
= – 2h (– 3h ) 4 9
(b) – 2h ( – 3h + 8h – 1 ) 4 9 2
+ (– 2h ) (8h )4 2 + (– 2h )(– 1)4
Example 1 (concluded) Find each product.
Multiply monomials.= 6h 13 – 16h 6 + 2h 4
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 7
5.3 Multiplying Polynomials
Multiplying Two Polynomials
Multiplying PolynomialsTo multiply two polynomials, multiply each term of the second polynomial by each term of the first polynomialand add the products.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 8
5.3 Multiplying Polynomials
Multiplying Two Polynomials
Distributive property( 2y – 5 ) ( 2y – 7y + 4 )2 3
= (2y )2 (2y )3 (–7y)(2y )2+ (4)(2y )2+
(–7y)+ (–5) (4)+ (–5)(–5)(2y )3+
= 4y 5 14y 3– 8y 2+ – 20+ 35y– 10y 3
= 4y 5 24y 3– 8y 2+ + 35y – 20 Combine like terms.
2 3Multiply 2 5 2 7 4 .y y y Example 2
5n + 8n – 3n – 23 2
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 9
5.3 Multiplying Polynomials
Multiplying Two Polynomials
4n + 32
– 6– 9n+ 24n 215n 3
– 8n 2– 12n 3+ 32n 420n 5
– 6– 9n+ 3n 3+ 32n 420n 5 + 16n 2
2 3 2Multiply 4 3 5 8 3 2 vertically.n n n n Example 3
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 10
5.3 Multiplying Polynomials
Multiplying Binomials by the FOIL Method
Multiplying Binomials by the FOIL Method
Step 1 Multiply the two First terms of the binomials to get the first term of the answer.
Step 2 Find the Outer product and the Inner productand add them (when possible) to get themiddle term of the answer.
Step 3 Multiply the two Last terms of the binomials to get the last term of the answer.
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 11
5.3 Multiplying Polynomials
Multiplying Binomials by the FOIL Method
F
( y – 4 ) ( 3y – 2 )
O
I
L
y ( 3y )
y ( – 2 )
– 4 ( 3y )
– 4 (– 2 )
= 3y – 2y – 12y + 82
= 3y – 14y + 82
F O I L
Example 4 Use the FOIL method to find 4 3 2 .y y
Multiply the last terms:
Multiply the inner terms:
Multiply the outer terms:
Multiply the first terms:
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 12
5.3 Multiplying Polynomials
Multiplying Binomials by the FOIL Method
F
( n – 7 ) ( 5n + 1 )
O
I
L
n ( 5n )Multiply the first terms:
n ( 1 )Multiply the outer terms:
– 7 ( 5n )Multiply the inner terms:
– 7 ( 1 )Multiply the last terms:
= 5n + n – 35n – 7 2
= 5n – 34n – 72
F O I L
Example 5 Multipy 7 5 1 .n n
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 13
5.3 Multiplying Polynomials
Multiplying Binomials by the FOIL Method
F
( 3g + 2 ) ( 9g – 4 )
O
I
L
3g ( 9g )Multiply the first terms:
3g ( – 4 )Multiply the outer terms:
2 ( 9g )Multiply the inner terms:
2 ( – 4 )Multiply the last terms:
= 27g – 12g + 18g – 8 2
= 27g + 6g – 82
F O I L
Example 6 (a) Find the product 3 2 9 4 .g g
Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 14
5.3 Multiplying Polynomials
Multiplying Binomials by the FOIL Method
F
( 6a + 3b ) ( 4a – 2b )
O
I
L
6a ( 4a )Multiply the first terms:
6a ( – 2b )Multiply the outer terms:
3b ( 4a )Multiply the inner terms:
3b ( – 2b )Multiply the last terms:
F O I L
= 24a – 12ab + 12ab – 6b 2 2
= 24a – 6b2 2
Example 6 (cont.) Find the product 6 3 4 2 .a b a b
