bell ringer mm1a2c & mm1a1h find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1)...
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![Page 1: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/1.jpg)
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
![Page 2: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/2.jpg)
Essential Question
![Page 3: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/3.jpg)
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?
![Page 4: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/4.jpg)
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.
![Page 5: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/5.jpg)
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.
![Page 6: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/6.jpg)
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?
![Page 7: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/7.jpg)
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!
![Page 8: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/8.jpg)
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
![Page 9: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/9.jpg)
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
![Page 10: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/10.jpg)
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!
![Page 11: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/11.jpg)
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
![Page 12: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/12.jpg)
6) Multiply: (y – 2)(y + 2)(y)2 – (2)2
y2 – 4
7) Multiply: (5a + 6b)(5a – 6b)
(5a)2 – (6b)2
25a2 – 36b2
![Page 13: BELL RINGER MM1A2c & MM1A1h Find the sum or difference. 1. (3m 3 + 2m + 1) + (4m 2 – 3m + 1) 2. (14x 4 – 3x 2 + 2) – (3x 3 + 4x 2 + 5) 3. Determine whether](https://reader033.vdocument.in/reader033/viewer/2022061305/55144639550346494e8b4bd8/html5/thumbnails/13.jpg)
HomeworkTextbook Page 70; 2 – 20 Even