Write

1
Write

• What are the key ideas involved in dealing with a
  situation like this one? What skills do you
  need? What math properties and ideas are in play?

2
Review 3 Addition and Multiplication

• Tuesday 15 January 2008

3
Review Week

• Friday Linear Equations
• Monday Systems
• Tuesday Multiplying Polynomials
• Wednesday Factoring Polynomials, Solving
• Thursday Solving Quadratics
• And Friday is a half-day.

4
Multiplication is Commutative and Associative
5
Exponent Rules for Multiplication

• These rules only apply if bases are the same, so
  work with one base at a time!!!

6
Good ideas

• Get rid of parentheses first.
• Changing order is legal.
• Exponents only apply to what they touch.
• Turn any negative exponents positive by
  'flipping' them.
• This is a matter of style, but it's usually a
  good idea.

7
Warm Ups
8
0 and Negative Exponents
9
A Rule for Dividing
10
A Few Examples

• Deal with parentheses first.
• Keep bases separate.
• Subtract.

11
Try Some
12
Polynomials and Monomials
13
The Degree of a Polynomial

• the degree of the highest degree monomial in the
  polynomial

14
Standard Form

• in order of decreasing degree

15
Like Terms
16
Adding Monomials

• Keep the variables exactly as they are.
• Add the coefficients.
• If it helps, think of each monomial as a kind of
  thing a puppy, a boot, a sammich.

17
Adding Polynomials

• Put like terms together.
• Nothing is attached to anything.
• Keep sign with term.
• Add.
• Put in standard form.

18
Subtracting Polynomials

• Switch signs on everything in the second
  polynomial.
• Really, youre distributing a -1.
• Put like terms together.
• Nothing is attached to anything.
• Keep sign with term.
• Add.
• Put in standard form.

19
Try a Few
20
The Distributive Property of Mult. Over Addition

• a (b c) ab ac
• The product of the sum with a
• equals
• the sum of the products with a.

21
Our Multiplication Rule
22
Distributing a Monomial

• Kick it in.
• Multiply each pair of monomials.
• Use addition rule on exponents.
• Watch signs!!!

23
A Slightly Tougher One
24
You Try One
25
Now Try a Few
26
Slightly Tougher
27
Try a Couple
28
Distributing a Monomial

• Kick it in.
• Multiply each pair of monomials.
• Use addition rule on exponents.
• Watch signs!!!

29
Multiplying 2 Polynomials

• Distribute.
• Distribute again.
• Multiply using the exponent addition property.
• As always, watch signs!!!

• (x 2)(x2 5x 4)

30
Try One
31
Now Try a Few

32
A Famous Shortcut
33
FOIL

• (4x 9) (-2x 8)
• Often, youll then be able to combine like terms.

34
You Try

• 1. (x 1) (x 1) 2. (m 5) (m 3)
• 3. (2 a) (3 a) 4. (2g a) (3g 4a)
• 5. (x m) (x m) 6. (3g2 4) (6g2 8)
• 7. (x x) (x x) 8. (7 3) (x 4)

35
Summary Addition and Multiplication Ideas

• What do we need to know?