Transcript 4.5 Notes Beginning Algebra

Chapter 4
Exponents
and
Polynomials
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-1
Chapter Sections
4.1 – Exponents
4.2 – Negative Exponents
4.3 – Scientific Notation
4.4 – Addition and Subtraction of Polynomials
4.5 – Multiplication of Polynomials
4.6 – Division of Polynomials
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-2
2
Multiplication of
Polynomials
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-3
3
Multiplying Polynomials
To multiply two monomials, multiply the coefficients
and use the product rule of exponents.
Example: (7x3)(6x5) = 7 · x36 · 6 · x5 = 42x8
To multiply a polynomial by a monomial, use the
distributive property: a(b + c) = ab + ac
Example: Multiply 3x(2x2 + 4)
3x(2x2 + 4) = (3x)(2x2) + (3x)(4) = 6x3 + 12x
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-4
4
Multiplying Polynomials
To multiply two binomials, use the distributive property
so every term in one polynomial is multiplied by
every term in the other polynomial.
Example:
a.) (x + 3)(x + 4) = (x + 3)(x) + (x + 3)(4) = x2 + 3x + 4x
+ 12 = x2 + 7x + 12
A common method used to multiply two binomials is the
FOIL method.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-5
5
The FOIL Method
Consider (a + b)(c + d):
F
O
I
Stands for the first – multiply the first terms together.
F
(a + b) (c + d):
product ac
Stands for the outer – multiply the outer terms together.
O
(a + b) (c + d):
product ad
Stands for the inner – multiply the inner terms together.
I
(a + b) (c + d):
product bc
Stands for the last – multiply the last terms together.
L
L
(a + b) (c + d):
product bd
The product of the two binomials is the sum of these four
products: (a + b)(c + d) = ac + ad + bc + bd
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-6
6
The FOIL Method
Using the FOIL method, multiply (2x - 3)(x + 4) .
L
F
(2x - 3)
(x + 4)
I
O
F
O
I
L
= (2x)(x) + (2x)(4) + (-3)(x) + (-3)(4)
= 2x 2
+ 8x
- 3x - 12
= 2x 2 + 5x - 12
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Chapter 4-7
7
Formulas for Special Products
Product of the Sum and Difference of the Same Two Terms
(a + b)(a – b) = a2 – b2
The expression on the right side of the equals sign is
called the difference of two squares.
Example:
a.)
(x + 5) (x – ) = x2 - 25
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-8
8
Formulas for Special Products
Square of Binomials
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
To square a binomial, add the square of the first term, twice the
product of the terms and the square of the second term.
Example:
a.) (x + 5)2 = (x)2 + 2(x)(5) + (5)2 = x2 + 10x + 25
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 4-9
9