1. 8-4 Multiplying Special Cases
Quiz tomorrow Wednesday 1/16
GVL Thursday 1/17 7pm
Test Friday 1/18
8-4 Multiplying Special Cases
Please work on the following problems on your notes (start before the bell rings):
Warm up:
Do the following for #1: #2: Multiply: (4x – 3)(x + 8)
a) Write in standard form
b) Leading term
c) Leading coefficient
d) Constant
e) Name the polynomial (by terms)
f) Name the polynomial (by degree)

2. #2: Multiply: (4x – 3)(x + 8)
Warm up:
Do the following for #1: a) Write in standard form b) Leading term c) Leading coefficient d) Constant e) Name the polynomial (by terms) f) Name the polynomial (by degree)

3. Today’s Objective Multiply (x + 3)2 vs (x + 3)(x – 3) (x + 3)(x + 3)
Answer:
Perfect Square Trinomial
Answer:
Difference of squares

4. Side Note: (x + 7)2 (x + 7)2 is NOT x2 + 49 (x + 7)2 is (x + 7)(x + 7)
Multiply by FOIL or Box Method x 7
x2 + 7x + 7x + 49 x x2 7x
x2 + 14x + 49 7x 7 49

5. What is the pattern? 3a 2 y 7 3a 9a2 6a
(y + 7)2 (3a + 2)2 y2 + 14y a2 + 12a + 4 (x – 6)2 (6x2 – 10y)2 x2 – 12x x4–120x2y+100y2 y y2 7y 2 6a 4 7 7y 49 x -6
6x2
-10y x x2
-6x
6x2
36x4
-60x2y
-6x 36
-10y -6
-60x2y
100y2

6. Special Cases a b Perfect Square Trinomial Square 1st
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
Square 1st
Multiply 1st & 2nd and double
Square 2nd a a2 ab b ab b2 a -b a a2
-ab -b
-ab b2

7. Examples Ex1) (x + 2)2 Think: (x)2 + 2(x•2) + (2)2 Answer: x2 + 4x + 4
(2y – 6)2
Think: (2y)2 – 2(2y•6) + (6)2
Answer: 4y2 – 24y + 36

8. What is the pattern? m -2n 6x -20 m m2 6x 36x2 2n 20 -400 x 6 x x2 6x
(m – 2n)(m + 2n) (6x + 20)(6x – 20) m2 – 4n2 36x (x – 6)(x + 6) (14x–9y)(14x+9y) x2 – x2–81y2
-2n 6x
-20 m m2
-2mn 6x
36x2
-120x 2n
2mn
-4n2 20
120x
-400 x 6 x x2 6x
14x
-9y -6
-6x
-36
14x
196x2
-126xy 9y
126xy
-81y2

9. Special Cases Difference of Squares Square 1st and 2nd and subtract! a
(a + b)(a – b) = a2 – b2
Square 1st and 2nd
and subtract! a -b a a2
-ab b ab
-b2

10. Examples Ex 3) (x + 5)(x – 5) Think: (x)2 – (5)2 Answer: x2 – 25 Ex 4)
(3x – 4y)(3x + 4y)
Think: (3x)2 – (4y)2
Answer: 9x2 – 16y2

11. TOO without Box method! 1) (x + 3)2 2) (a – 2)2
Perfect Square Trinomial
1) (x + 3)2 2) (a – 2)2
(2y + 5)2 4) (3m + 6n)2
5) (k + 1)(k – 1) 6) (3r + 5)(3r – 5)
7) (4c + d)(4c – d) 8) (p2 – 2q2)(p2 + 2q2)
Answers:
1) x2 + 6x ) a2 – 4a + 4
3) 4y2 + 20y ) 9m2 + 36mn + 36n2
5) k2 – 1 6) 9r2 – 25
7) 16c2 – d2 8) p4 – 4q4
Difference of squares

12. Homework Delta Math You can finish ALL sections Due Friday
Quiz tomorrow Wednesday 1/16
GVL Thursday 1/17 7pm
Test Friday 1/18
Homework
Delta Math
You can finish ALL sections
Due Friday

13. Extra Mental Math 482 Change to (40 + 8)2 or (50 – 2)2
(40)(8) + 82
2304
TOO: NO CALCULATOR
91204
(50)(2) + 22
2500 –
2304

14. Mental Math 79•81 Change to (80 – 1)(80 + 1) 802 – 12 6400 – 1 6399
TOO: 398•402 NO CALCULATOR
91204