Drill #17 Simplify each expression.

Drill #18 Simplify each expression.

Drill #19 Simplify each expression.

Drill #20 Simplify each expression.

Drill #21 Simplify each expression.

Drill #22 Simplify each expression.

Drill #23 Simplify each expression.

Drill #24 Simplify each expression.

Drill #18 Simplify each expression. State the degree and coefficient of each simplified expression:

6-1 Operations With Polynomials Objective: To multiply and divide monomials, to multiply polynomials, and to add and subtract polynomial expressions.

Negative Exponents * For any real number a and integer n, Examples:

Example: Negative Exponent *

Product of Powers * For any real number a and integers m and n, Examples:

Example: Product of Powers*

Quotient of Powers * For any real number a and integers m and n, Examples:

Example: Power of a Power*

Power of a Power* If m and n are integers and a and b are real numbers: Example:

Example: Power of a Power*

Power of a Product* If m and n are integers and a and b are real numbers: Example:

Example: Power of a Product*

Power Examples* Ex1: Ex2: Ex3:

Find the value of r Find the value of r that makes each statement true:

Find the value of r * Find the value of r that makes each statement true:

Monomials* Definition: An expression that is 1) a number, 2) a variable, or 3) the product of one or more numbers or variables. Constant: Monomial that contains no variables. Coefficients: The numerical factor of a monomial Degree: The degree of a monomial is the sum of the exponents of its variables.

State the degree and coefficient * Examples:

Polynomial* Definition: A monomial, or a sum (or difference) of monomials. Terms: The monomials that make up a polynomial Binomial: A polynomial with 2 unlike terms. Trinomial: A polynomial with 3 unlike terms Note: The degree of a polynomial is the degree of the monomial with the greatest degree.

Polynomials Determine whether each of the following is a trinomial or binomial…then state the degree:

Like Terms* Definition: Monomials that are the same (the same variables to the same power) and differ only in their coefficients. Examples:

Adding Polynomials* To add like terms add the coefficients of both terms together Examples

To combine like terms To add like terms add the coefficients of both terms together Example

Subtracting Polynomials* To subtract polynomials, first distribute the negative sign to each term in the polynomial you are subtracting. Then follow the rules for adding polynomials. EXAMPLE:

Multiplying a Polynomial by a Monomial* To multiply a polynomial by a monomial: 1. Distribute the monomial to each term in the polynomial. 2. Simplify each term using the rules for monomial multiplication.

FOIL* Definition: The product of two binomials is the sum of the products of the F the first terms Othe outside terms Ithe inside terms Lthe last terms F O I L (a + b) (c + d) = ac + ad + bc + bd

The Distributive Method for Multiplying Polynomials* Definition: Two multiply two binomials, multiply the first polynomial by each term of the second. (a + b) (c + d) = c ( a + b ) + d ( a + b )

Examples: Binomials

The FOIL Method (for multiplying Polynomials)* Definition: Two multiply two polynomials, distribute each term in the 1 st polynomial to each term in the second. (a + b) (c + d + e) = (ac + ad + ae) + (bc + bd + be)

The Distributive Method for Multiplying Polynomials* Definition: Two multiply two polynomials, multiply the first polynomial by each term of the second. (a + b) (c + d + e) = c ( a + b ) + d ( a + b ) + e ( a + b )

Examples: Binomials x Trinomials

Classwork: Binomials x Trinomials

Pascals Triangle (for expanding polynomials)