BELL RINGER MM1A2c & MM1A1h

Find the sum or difference.

1. (3m3 + 2m + 1) + (4m2 – 3m + 1)

2. (14x4 – 3x2 + 2) – (3x3 + 4x2 + 5)

3. Determine whether the function

f(x) = is even, odd, or neither.xx 82 3

Essential Question

Daily Standard & Essential Question

• MM1A2c :Add, subtract, multiply, and divide polynomials

• MM1A2g: use area and volume models for polynomials arithmetic

• Essential Question: What are the three special products and how can you quickly find each one?

There are formulas (shortcuts) that work for certain polynomial

multiplication problems.

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a - b)(a + b) = a2 - b2

Being able to use these formulas will help you in the future when you have to factor. If you do not remember the formulas, you can always multiply using distributive,

FOIL, or the area model method.

Let’s try one!1) Multiply: (x + 4)2

You can multiply this by rewriting this as (x + 4)(x + 4)

ORYou can use the following rule as a shortcut:

(a + b)2 = a2 + 2ab + b2

For comparison, I’ll show you both ways.

1) Multiply (x + 4)(x + 4)

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

x2 +8x + 16

x +4

x

+4

x2

+4x

+4x

+16

Now let’s do it with the shortcut!

x2

+4x+4x+16

Notice you have two of

the same answer?

1) Multiply: (x + 4)2

using (a + b)2 = a2 + 2ab + b2

a is the first term, b is the second term(x + 4)2

a = x and b = 4Plug into the formula

a2 + 2ab + b2

(x)2 + 2(x)(4) + (4)2

Simplify.x2 + 8x+ 16

This is the same answer!

That’s why the 2 is in

the formula!

2) Multiply: (3x + 2y)2

using (a + b)2 = a2 + 2ab + b2

(3x + 2y)2

a = 3x and b = 2y

Plug into the formulaa2 + 2ab + b2

(3x)2 + 2(3x)(2y) + (2y)2

Simplify9x2 + 12xy +4y2

Multiply: (x – 5)2

using (a – b)2 = a2 – 2ab + b2

Everything is the same except the signs!

(x)2 – 2(x)(5) + (5)2

x2 – 10x + 25

4) Multiply: (4x – y)2

(4x)2 – 2(4x)(y) + (y)2

16x2 – 8xy + y2

5) Multiply (x – 3)(x + 3)

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

x2 – 9

x -3

x

+3

x2

+3x

-3x

-9

This is called the difference of squares.

x2

+3x-3x-9

Notice the middle terms

eliminate each other!

5) Multiply (x – 3)(x + 3) using (a – b)(a + b) = a2 – b2

You can only use this rule when the binomials are exactly the same except for the sign.

(x – 3)(x + 3)

a = x and b = 3

(x)2 – (3)2

x2 – 9

6) Multiply: (y – 2)(y + 2)(y)2 – (2)2

y2 – 4

7) Multiply: (5a + 6b)(5a – 6b)

(5a)2 – (6b)2

25a2 – 36b2

HomeworkTextbook Page 70; 2 – 20 Even