Simple

1. FACTORIZATION:
GRADE: 9 TEACHER’S NAME: RANA FLEIHAN-AMMOURI

2. FACTORIZE BY TAKING A COMMON FACTOR:
36𝑥2
𝑦 + 16𝑥𝑦
= 2.2. 𝑥. 𝑦 9𝑥 + 4
= 4𝑥𝑦 9𝑥 + 4 .
Thin
k
(3x+1)(2x-3)+(x-6)(2x-3)
= (2x-3)[(3x+1)+(x-6)]
= (2x-3) [ 3x+1+x-6]
= (2x-3)[4x-5]
(3x+1)(2x-3)+(x-6)(2x-3)
.2.

3. NEW EXAMPLE[ COMMON FACTOR]

4. BY USING THE PERFECT SQUARE:
 𝟗𝒙𝟐 + 𝟏𝟐𝒙 + 𝟒 = 𝟑𝒙 + 𝟐 𝟐
 𝟗𝒙𝟐 − 𝟏𝟐𝒙 + 𝟒 = 𝟑𝒙 − 𝟐 𝟐
 Try to solve the following:
 𝟑𝟔𝒚𝟐
+ 𝟏𝟖𝒚 + 𝟗 = ⋯ 6𝑦 + 3 2

5. USING DIFFERENCE OF TWO SQUARES:
𝒂𝟐
− 𝒃𝟐
= (𝒂 − 𝒃)(𝒂 + 𝒃)
 Simple example:
 9𝑥2
− 49 = (3𝑥 − 7)(3𝑥 + 7)
 Harder a little…….
 9𝑥2
− 𝑥 + 2 2
 = 3𝑥 − 𝑥 + 2 3𝑥 + 𝑥 + 2
 = 3𝑥 − 𝑥 − 2 3𝑥 + 𝑥 + 2
 = 2𝑥 − 2 [4𝑥 + 2]
 You can take common factors too…
 = 2 𝑥 − 1 2 2𝑥 + 1
 = 4(𝑥 − 1) (2𝑥 + 1)

6. BY GROUPING:
 𝑥2 − 2𝑥 + 𝑥𝑦 − 2𝑦
 𝑥2 + 𝑥𝑦 − 2x − 2y … … . . grouping
 𝑥 𝑥 + 𝑦 − 2 𝑥 + 𝑦 … . . 𝑐𝑜𝑚𝑚𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟
 𝑥 + 𝑦 𝑥 − 2 … … … … . . 𝑐𝑜𝑚𝑚𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟.

7. FURTHER PRACTICE:
EXERCISES
BOOK 8
ANSWERS

8. NUMBER:8

9.  You can take common factors too…
 = 2𝑥 + 3 𝑥 − 1 − 1 − 𝑥 2𝑥 + 1
 2𝑥 + 3 𝑥 − 1 + 𝑥 − 1 2𝑥 + 1 =
𝑥 − 1 2𝑥 + 3 + 2𝑥 + 1
 𝑥 − 1 2𝑥 + 3 + 2𝑥 + 1
 = 𝑥 − 1 4𝑥 + 4 = 4(x − 1)(x + 1)