FactoringSession 6:Factoring Special Forms-Perfect Square Trinomial (PST)- -Difference of Two Squares (DoTS)

Practice Test 2 –NOV. 18

UNIT QUIZ 1 – Nov. 22 GCF, Grouping, DoTS, PST

OBJECTIVE:

Factorize algebraic expression using DoTS.

Factorize algebraic expression using SoB.

Factoring Special Forms

Perfect Square Trinomials

222 2 )1 BABABA

222 2 )2 BABABA

A2 + 2AB + B2 = (A + B)2

A2 - 2AB + B2 = (A - B)2

Perfect Square Trinomials

1st and last terms are perfect squaresmiddle term is 2x the product of the square roots of 1st & last terms

Factor x2 + 10x + 25

x2 + 10x + 25 = (x)2 + 2(5x) + (5)2 = (x + 5)2

Factor x2 - 12x + 36

x2 - 12x + 36 = (x)2 – 2(6x) + (6)2 = (x - 6)2

A2 +2AB + B2 (A+B)2

Perfect Square Trinomials

Factor the following:1) 16x2 – 40xy + 25y2

2) 100x2 + 180x + 81

3) 3+6b+3b2

4) 10n2 +100n+250

5) 49n2 −56n+16

6) 200m4 + 80m3 + 8m2

The Difference of Two Squares

The Difference of Two Squares

The difference of the squares of two terms, factors as the product of a sum and a difference of those terms.

. 22 BABABA

Factor x2 - 25

x2 - 25 = x2 – 52 = (x + 5) (x – 5)

Factor 9x2 - 4y2

9x2 - 4y2 = (3x)2 – (2y)2 = (3x + 2y) (3x - 2y)

The Difference of Perfect Squares

Factorize the following:

k2 – 81 = k2 – 92

(k – 9)(k + 9)

Sum and Difference of Two Squares (DoTS)

(x – y)(x + y) = x2 – y2

Factorize the following:

9a2 – 4

Sum and Difference of Two Squares (DoTS)

(x – y)(x + y) = x2 – y2

Factorize the following:

25a2 – 64

Sum and Difference of Two Squares (DoTS)

(x – y)(x + y) = x2 – y2

Factorize the following:

x2 – 16

Sum and Difference of Two Squares (DoTS)

(x – y)(x + y) = x2 – y2

Factor the following completely

1)4m2 −25

2)9x2 − 1

3)98n2 −200

4)400 − 36v2

5)6x2 – 6y2

Seatwork: (Notebook)

NSM Book 2: page 91, Exercise 3e:

☞ no. 3, letters f – j ☞ no. 4, letter g – i

Seatwork: no. 3 (f – j)

f) 81 – 16x2

g) 64 – 9a2

h) –4h2 + 81

i) 2x2 – 18

j) 3x2 – 147

Seatwork: no. 4 (g – i)

e) 3x2 – 27y2

f) 64a2 – 4b2

g) k2 – ¼ h2

SEATWORK (Notebook)

Warm-up: (Notebook)

NSM Book 2: page 92, Exercise 3e:

☞ no. 7, letters a – j

Factor the following completely1)

2) 8r3 −64r2 +r −8

3) 63n3 +54n2 −105n−90

4) 42mc + 36md − 7n2c − 6n2d

.xxx 2793 23

PRACTICE TEST25 MINS

Evaluate the following by factorization:

79 83 – 69 83

= 83 (79 – 69)

= 83 (10)

= 830

Evaluate the following by factorization:

1032 – 9= (103 + 3)(103 – 3)

= (106)(100)

= 10,600

Evaluate the following by factorization:

592 – 412

Evaluate the following by factorization:

682 – 322

Evaluate the following by factorization:

7.72 – 2.32

Evaluate the following by factorization:

26.72 – 23.32

Seatwork: (Notebook)

NSM Book 2: page 92, Exercise 3e:

☞ no. 5, letters f – j☞ no. 6, letters b, d and f

Seatwork: no. 5 (f – j)

f) 2562 – 1562

g) 8922 – 82

h) 9032 – 972

i) 7632 – 2372

j) 6592 – 3412

Seatwork: no. 6

b) 5.16 5.6 + 5.16 4.4

c) 587 23 – 23 487

d) 842 – 84 74

HOMEWORKReview Questions 3 page 108 # 2. a – j # 3. a – j1 whole pad paperSTUDY FOR A UNIT TEST ON TUESDAY