德望學校 – S2數學 2A Chapter 2 Identities and Factorization – CQ (11-16)

試卷答案:

1. –
2. a = 3, b = 6
3. (6 – r)(k – 1) or (1 – k)(r – 6)
4. a) (2x – 5y)²
   b) (25y + 2x – 5y)(25y – 2x + 5y)
5. \(\dfrac{w^{4}}{16} – \dfrac{4}{9}\)
6. A =2. B = 3, C = -1
7. a) 36m² – 24m + 4
   b) \(\dfrac{4b^{2}}{a^{2}} – \dfrac{49a^{2}}{b^{2}}\)
8. a) 2x²y (1 + 3y)(1 – 3y)
   b) 2x² (1 – 3y)( y(1 + 3y) + 2)
9. It is an identity.
10. a) (a + b + c)(1 – p)
    b) (1 – x)(5x + 7y)
11. (y + 4x + 1)(y – 4x – 1)
12. A = -1, B = 0, C = 4
13. a) 4a⁴ – 121
    b) 25a² + 5a + 1/4
14. a) (m – n)(1 + k)
    b) 2a(5a + 3b))5a – 3b)
15. It is an identity.
16. A = 1, B = 1, C = -2
17. a) (x + b)(ax – 1)
    b) 2 (9x + y)(9x – y)
18. a) 12.5x² + 20x + 8
    b) (y + 1)² (x + 2y – 2)(x – 2y + 2)
19. a) 18x² + 48x + 32
    b) x²/4 – y²/9
20. It is an identity.
21. a) (6x + 1)²
    b) (7y – 2)²
    c) (6x + 7y – 1)(6x – 7y + 3)
22. A = 0, B = 1, C = -4
23. a) 18x² + 48x + 32
    b) x²/4 – y²/9
24. It is an identity.
25. a) (6x + 1)²
    b) (7y – 2)²
    c) (6x + 7y – 1)(6x – 7y + 3)
26. A = 0, B = 1, C = -4
27. It is not an identity.
28. A = -4, B = 1
29. a) \(\dfrac{1}{4}(2x+1)(2x-1)\)
    b) (x² + 1/4)(x + 1/2)(x – 1/2)
30. a) (x – 6)²
    b) x² – 6x + 9
    c) Yes, I agree.
31. a) \(\dfrac{x^{2}}{4}+\dfrac{xy}{3}\dfrac{y^{2}}{9}\)
    b) (x² + 4)(x² + 4x – 4)
32. A = 1, B = 2, C = -3
33. a) It is an identity.
    b) (x + y)(x + y – z)
34. a) (3a + 4b)(3a – 4b)
    b) -7 (m – n)²⁰¹⁴
35. a) (2x – 1)(x – 5)
    b) (x – 5)(2xy – 2x + 1)
36. a) 2 (2a + 3b)(2a – 3b)
37. A = -1, B = -1
38. It is an identity.
39. a) 2(2x +5)(2x – 5)
    b) (2x – 5)(4x + 10 + y)
40. A = -6, B = 1
41. a) (x + y)(A + B + C)
    b) -2y (y – x)
42. A = 4, B = -4

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