# Mathematics Secondary Four Factorization by AL5oUKlK

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```									Mathematics               Secondary Four
Factorization
Exercises A                Level 1
Factorize each of the following expressions. If not possible, say so. (No. 1 – 39)
1. x2 + 3x + 2                2. a2 + 4a +3                   3. x2 + 7x + 12
4. m2 + 6m + 8                5. x2 + 9x + 14                6. x2 – 3x + 2
7. x2 + 8x + 15               8. x2 + 11x + 10               9. x2 – 7x + 12
10. x2 – 7x + 10             11. x2 – 11x + 28              12. x2 + 2x – 35
13. x2 – x – 6               14. x2 – 2x – 15               15. x2 + 2x – 48
16. x2 – x – 42              17. x2 + x – 20                18. a2 – 3a – 40
19. a2 – 6a – 27             20. m2 + 3m – 54               21. h2 – 3h – 40
22. b2 – 19b + 90            23. n2 – 15n – 16              24. b2 – 8b – 20
25. t2 – 5t – 36             26. n2 + 8n – 48                27. n2 + 11n – 26
28.   m2 + 4m – 96           29.    m2 – 30m – 99           30.     c2 + 5c – 84
31.   a2 – ab – 6b2          32.    m2 + mn – 12n2          33.     h2 – 13hk + 36k2
34.   r2 – 3rs – 48s2        35.    x2 – 3xy + 2y2          36.     s2 – 20st + 64t2
37.   2t2 – 2t – 40           38.    2x2 – 10x – 48         39.     3a2 – 3a – 396

Exercises B
Level 1
Factorize each of the following expressions. If not possible, say so. (No. 1 – 40)
1. 2x2 + 3x + 1               2. 2a2 + 5a + 3                3. 4m2 + 6m + 2
4. 2x2 + 7x + 5               5. 3x2 – 5x – 2                 6. 2x2 + 9x – 5
7. 2x2 – 3x – 5               8. 5x2 – 8x + 3                 9. 2t2 + 7t – 4
10.   21x2 + 11x – 2          11.   3a2 – 12a + 12           12.    3x2 + x – 10
13.   3x2 – 16x – 12          14.   6x2 –x – 12               15.    2x2 –x – 6
16.   6t2 – 11t + 3           17.   4x2 + 2x – 12             18.    9x2 + 5x – 4
19.   2m2 – 3m – 35           20.   24x2 + 10x – 4            21.    8x2 – 14x – 15
22.   30x2 – 23x + 2          23.   8x2 – 26x + 15            24.    4x2 – 12x + 9
25.   25x2 – 10x + 1          26.   3x2 – 14x + 15            27.    12x2 + 25x + 12
28.   6a2 – 2a – 4            29.   4x2 – 18x + 20           30.    12 – 20c – 8c2
31.   8k2 – 22k + 12          32.   12c2 – 22c + 6           33.    8r2 + 7r – 15
34.   16m2 – 24m + 9          35.   42x2 –x – 30             36.    4x3 – 8x2 – 60x

Level II
37. 4s2 + 15rs + 14r2         38. 2a2 – 11ab + 15b2           39. 21x2 – 17xy + 2y2
40. 28p2 – 13pq – 5q2
41. Factorize (a)        3x2 – 12x + 12
(b)      3(x2 – x)2 – 12(x2 – x) + 12
42. Factorize (a)        2x2 – 44x + 80
(b)      2(x2 + x)2 – 44(x2 + x) + 80
Buddhist Yip Kei Nam Memorial College
Secondary Four
Mathematics Exercises
(I)    Algrbraic expression
A. Expand the following expression
1. – 2(3a – b)            2. – 3(1 – 2m + n)        3. 2a(3 – a)
4. – 3(2x + 3y – z)       5. 3a(4a – b + 2c)        6. (2a – b + 2c)a
2        2               2
7. (2xy)(x – xy + y )     8. (– 2a)(a – 3a + 2)     9. (abc)(1 – a + b – c)
2 2
10. (– 2ax)(3x y + 6xy + 2ax)                    2
11. (y – 2xyz + 2x2z2)(– 3xyz)
12. – 8(x2 – 2x + 5)      13. b2 (– a + 2b – c)     14. (p – 4q + r)( – 3r)
3   2
15. (– 2x )(x – 2x + 1) 16. 2x – 3(2 – x)           17. 4(3x – 1) + 3(1 – 2x)
18. t(17 – t) + t (4 – t) 19. a(5 +a) – a(a – 2)    20. m(m + 1) – m(m – 3)
21. 2x(5 –x) – x(x + 6)

B.      Expand the following expression
1.    (a + b)(c – d)        2. (x + 3)(x – 4)              3.    (x + 2y)(x – y)
4.    (h – 5)(h + 7)        5. 9(n + 2)(2n – 3)            6.    (2y + 3)(4 – 5y)
7.    (2x – y)(2y – x)      8. (x – 2y)(3a – 2b)           9.    (x + 5)(x – 5)
10.    (2y – 3)(2y + 3)     11. 5(x – 6)(x + 6)            12.    (x – 10)(x + 10)
13.    (7 + y)(7 – y)       14. (– 2 – x) (– 2 + x)        15.    (2u + 3) (2u – 3)
16.    (–2a + 3b)( –2a – 3b) 17. (6 – 5c )(6 + 5c)         18.    (x + 5)2
19.    (8y – 3)2            20. (2x + 7)2                  21.    (2 – 3b)2
22.    (3 + 5y)2

(II)   Factorization
A. x2 – y2 = ( x + y ) ( x – y )
1. z2 – 4                  2. 4x2 – 1                3.         9x2 – 16y2
2                          2
4. 144 – a                 5. 64 – 4k                6.         2x2 – 2y2
2          2
7. (a + 2) – (a + 1)                        2
8. (b – 3) – (4 – b)2
9. 144x2 – a2b2           10. 9b2c2 – 16             11.        125 – 5x2
2 2               3      2
12. 32 – 72s t           13. a – 4ab                 14.        (x +1)2 – 49
2         2                          2
15. 4(x – 1) – (y – 1)             16. 1 – (x – 5)

B.     x2 + 2xy + y2 = ( x + y )2
x2 – 2xy + y2 = ( x – y )2
1. a2 + 4ab + b2            2. x2 – 10x + 25          3. a2 + 6a + 9
4. 1 + 4x + 4x2             5. b2 – 2b + 1            6. 4 – 12y + 9y2
7.    25h2 – 10h + 1           8. 9 – 24k + 16k2        9. y2 – 18 y + 81
10.    18m2 + 12m + 2          11. 49m2 + 56m + 16        12. 3y2 – 18xy + 27x2
13.    3y2 – 18y + 27           14. 12u2 – 36u + 27        15. 8x2 + 56x + 98
16.    (x + y)2 – 2(x + y) + 1            17. (3x + y)2 + 4(3x + y) + 4
18.    (x + y)2 + 10(x + y) + 25

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