1. Exponents and Polynomials

2. 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
Chapter 1 Outline

3. Multiplication of Polynomials

4. 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

5. 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.

6. The FOIL Method F O I L Consider (a + b)(c + d):
Stands for the first – multiply the first terms together.
(a + b) (c + d): product ac
Stands for the outer – multiply the outer terms together.
(a + b) (c + d): product ad O
Stands for the inner – multiply the inner terms together.
(a + b) (c + d): product bc I
Stands for the last – multiply the last terms together. 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

7. The FOIL Method Using the FOIL method, multiply (2x - 3)(x + 4) .
+ (-3)(4) L
= (2x)(x)
(2x - 3) (x + 4) F
+ (-3)(x) I O
+ (2x)(4)
= 2x x x
= 2x 2 + 5x - 12

8. 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

9. 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