Warm Up 1) Create the following: 2) Create a Monomial, Binomial, and Trinomial 3) Find the Degree of the following a) 5x - 10 b) 6x 2 + 3x - 1 4) Find the Degree and put in Standard Form: 5x 5 + 3x x 2 + 3x 4 – 1 5) Find the sum/difference: a) (9x 4 + 8y + 12) – (3y 2 – 7y + 2) b) ( 6x 3 + 5x +11) + ( 3x 3 +7x +8) Constant Linear Equation Quadratic Equation Cubic Equation

Review  How would you multiply 3(5x – 1) ?  Can we classify these polynomials?

Multiplying a MONOMIAL and a POLYNOMIAL  Two things to remember: 1. Use the DISTRIBUTIVE PROPERTY! 2. When multiplying variables, ADD the exponents. Example:

Examples:

You try:

Examples:

You try:

Examples:  What is different here?

You try:

Examples:  You want to find the area of the classroom. Your teacher tells you that the length is 5 feet less than twice the width. Write a single polynomial to express the area of the room.

You try:  A rectangular garden is 2x + 3 units long and 3x units wide.  A) Draw a model of the garden.  B) Find the area of the garden.

Hands up, pair up  Walk around the room, high-fiving your classmates. When I say “pair up,” the person that you are high-fiving becomes your partner. Sit down together and wait quietly for the next instructions.

Partner Ticket Out  Simplify the following: 1. 2.

Homework  1.5 Study Guide Worksheet

January 31 st, 2013

Warm Up 1. Multiply: 2. Multiply: 3. Simplify: 1. Find the area of the rectangle:

Summarize  What types of polynomials have we already multiplied?  What property did we use to multiply them?

Can we classify these 2 polynomials? (2x + 3)(5x + 8)

Multiplying a BINOMIAL and a BINOMIAL  Guess what: we STILL use the DISTRIBUTIVE PROPERTY.  But we also have some special tricks to make distributing easier: FOIL Box Method

FOIL  FOIL is an acronym that can help you multiply two binomials.  F – First  O – Outside  I – Inside  L – Last

Let’s see how it works… (y + 3)(y + 7)

Examples: (2x + 3)(5x + 8)

Examples: (2x – 1)(-4x + 4)

You try: (8x + 1)(x – 3)

You try: (5x – 3)(10x – 2)

Why is FOIL the same as the Distributive Property?

Box Method  The box method is more visual and can help you make sure that you have not missed multiplying any terms.

Box Method  Draw a box and write one binomial on the top and the other on the bottom.  Multiply each pair of terms.  Your answer is on the inside of the box. Combine like terms to write your final answer. Example: (3x – 5)(5x + 2)

Example: (7p – 2)(3p – 4)

Example: (2a – 3b)(2a + 4b)

You try: (6p – 4)(p + 10)

You try: (p – 3)(4p – 7)

Why is the Box Method the same as the Distributive Property?

A Binomial SQUARED What does it mean to SQUARE a number? How could we simplify the expression (4x + 1) 2 ?

You try:  Use either method to simplify the following: (2x – 3) 2

Writing assignment  Tell whether you prefer to multiply binomials using the FOIL method or the Box method. Explain why you prefer that method in 2-3 sentences.

Practice Time  Cut the DARK squares apart.  Multiply each pair of binomials and match your answer to another square.  When you think you have matched all of the squares, let me know and I will come check your work. If it is correct, I will bring you paper and glue to glue down your puzzle.

Homework  Quotable puzzle – you must show your work!

February 1 st, 2013

Warm Up 1. Find the area of the rectangle below: 2. Find the area of a SQUARE with side length (x + 3)

Summarize  What type of polynomials have we multiplied so far?

Can we classify the polynomials below? (3x + 7)(2x 2 – x + 5)

How can we multiply them? (3x + 7)(2x 2 – x + 5)

Example: (r – 2)(3r 2 + 4r – 1)

Example: (4ab – 2a + 3)(a + b)

You try: (5x + 2)(3x 2 – 8x + 10)

You try:  Find the area of the rectangle below:

Write your own  Create 3 problems for your partner to simplify: 1. MONOMIAL times a BINOMIAL 2. BINOMIAL times a BINOMIAL 3. BINOMIAL times a TRINOMIAL

Instructions  Now on a separate sheet, you should simplify each expression.  Once you both are finished simplifying your own expression, exchange the problems (without the work) with your partner.  Simplify your partners expressions then exchange back and check each others’ work.

Put it all together  Simplify: 3a(a 2 – 4) + 5a 2 (2a + 10)

You try!  Simplify: -4b(2b + 1) – 8(b 2 + 2b – 2)  Simplify: x 2 (x + 1) + 5x(x – 3) – 4(x + 10)

Multiplication practice

Around the World  I will assign your group and tell you where to begin.  Lift up the flap and simplify the expression underneath. Look for your answer somewhere else around the room and go there to complete the next problem.  The problems form a circuit. If you have done everything correctly, you should end up where you begin.  Be sure to show your work for every problem. This is how you will earn your QUIZ grade.

Ticket Out On a separate sheet of paper, simplify each of the following: 1. (8x – 2) 2 2. (5x + 6)(x 2 – 2x + 5) 3. Write 3-5 sentences explaining to your friend how to multiply polynomials.

Homework  Workbook p. 232 (#35-41)