4 1.

2ax2-3x+2ax-3= .

42.

9x2-66x+ 12 1= .

43. Factorization 8-2x2 =.

44. Factorization x2-x+ 14 =.

45. Factorization 9X2-30x+25 =.

46. Factorization -20x2+9x+20 =.

47. Factorization 12x2-29x+ 15 =.

48. Factorization is 36x2+39x+9 =.

49. Factorization 2 1x2-3 1x-22 =.

50. Factorization 9x4-35x2-4 =.

5 1. Factorization (2x+1) (x+1)+(2x+1) (x-3) =.

52. Factorization 2ax2-3x+2ax-3 =.

53. Factorize X (y+2)-X-Y- 1 =.

54. Factorization (x2-3x)+(x-3) 2 =.

55. Factorize 9X2-66x+ 12 1 =.

56. Factorization 8-2x2 =.

57. Factorize x4- 1 =.

58. Factorization x2+4x-xy-2y+4 =.

59. Factorization 4x2- 12x+5 =.

60. Factorization 2 1x2-3 1x-22 =.

6 1. Factorization 4x2+4xy+y2-4x-2y-3 =.

62. Factorization 9X5-35x3-4x =.

63. Break down the following categories:

( 1)3x2-6x= .

(2)49x2-25= .

(3)6x2- 13x+5= .

(4)x2+2-3x= .

(5) 12x2-23x-24= .

(6)(x+6)(x-6)-(x-6)= .

3(x+2)(x-5)-(x+2)(x-3)= .

(8)9x2+42x+49= .

( 1)(x+2)-2(x+2)2= .

(2)36x2+39x+9= .

(3)2x 2+ax-6x-3a = 1 .

(4)22x2-3 1x-2 1= .

70. Factorization 3ax2-6ax= =.

7 1. Factorization (x+ 1) x-5x =.

72. Factorization (2x+1) (x-3)-(2x+1) (x-5) =1

73. Factorization xy+2x-5y- 10 =

74. Factorization X2Y2-X2-Y2-6xy+4 =

x3+2x2+2x+ 1

a2b2-a2-b2+ 1

( 1)3ax2-2x+3ax-2

(x2-3x)+(x-3)2+2x-6

1)(2x+3)(x-2)+(x+ 1)(2x+3)

9x2-66x+ 12 1

17. Factorization

( 1)8 x2- 18(2)x2-(a-b)x-ab

18. Break down the following categories

( 1)9 x4+35 x2-4(2)x2-y2-2yz-z2

(3)a(b2-c2)-c(a2-b2)

19. Factorization (2x+1) (x+1)+(2x+1) (x-3)

20. Factorization 39x2-38x+8

2 1. Find the value of (65 12) 2-(34 12) 2 by factorization.

22. Decomposition A (B2-C2)-C (A2-B2)

24. Factorization 7 (x-1) 2+4 (x-1) (y+2)-20 (y+2) 2.

25. decompose xy2-2xy-3x-y2-2y- 1

26. Factorization 4x2-6ax+ 18a2

27. decompose 20a3bc-9a2bc-20ab3c

28. Factorization 2 x2-5x+2ax-5

29. Factorization 4x3+4x2-25x-25

30. Factorization (1-xy) 2-(y-x) 2

3 1. factorization

( 1)mx2-m2-x+ 1(2)a2-2ab+B2- 1

32. Break down the following categories

( 1)5x 2-45(2)8 1x 3-9x(3)x2-y2-5x-5y(4)x2-y2+2yz-z2

33. Factorization: xy2-2xy-3x-y2-2y- 1

34. Factorize Y2 (x-y)+Z2 (y-x)

1) factorization x2+x+y2-y-2xy =

35. Factorization x2-25 =.

36. Factorization x2-20x+ 100 =.

37. Factorization x2+4x+3 =.

38. Factorization 4x2- 12x+5 =.

39. Break down the following categories:

( 1)3ax2-6ax= .

(2)x(x+2)-x= .

(3)x2-4x-ax+4a= .

(4)25x2-49= .

(5)36x2-60x+25= .

(6)4x2+ 12x+9= .

(7)x2-9x+ 18= .

(8)2x2-5x-3= .

(9) 12x2-50x+8= .

(1) answer: a(b? 1)(ab+2b+a)

Description: (ab+b)2? (a+b)2 = (ab+b+a+b)(ab+b？ Answer? b) = (ab+2b+a)(ab？ a) = a(b？ 1)(ab+2b+a)。

(2) answer: (x? a)4

Description: (a2? x2)2？ 4ax(x？ a)2

= [(a+x)(a？ x)]2？ 4ax(x？ a)2

= (a+x)2(a？ x)2？ 4ax(x？ a)2

= (x？ a)2[(a+x)2？ 4ax]

= (x？ a)2(a2+2ax+x2？ 4ax)

= (x？ a)2(x？ a)2 = (x？ A) 4.

(3) Answer: 7xn? 1(x？ 1)2

Description: Original formula = 7xn? 1 ? x2？ 7xn？ 1 ? 2x+7xn？ 1 = 7xn？ 1(x2？ 2x+ 1) = 7xn？ 1(x？ 1) 2. 1. When observing an object with a microscope, the image formed by the objective lens is an enlarged _ _ _ _ _ _ _ _ _ _ (fill in "virtual" or "real") image, just like the lens imaging of _ _ _ _ _ _ _.

Thinking analysis: The principle of microscope imaging tells us that the object passes through the objective lens and becomes an inverted magnified real image. The real image is within the focus range of the eyepiece, and then becomes an upright magnified virtual image through the eyepiece. Objective imaging is the same as camera lens, and the eyepiece acts as a magnifying glass.

Answer: The real camera magnifies the mirror.

2.(20 10 simulation in Guiyang, Guizhou) If you want to observe the internal structure of a leaf carefully, you'd better use ().

A. plane mirror B. concave lens C. magnifying glass D. microscope

Thinking analysis: the plane mirror becomes a virtual image of the same size, without magnification, A is wrong. Concave lenses can't magnify objects, and B is wrong. A magnifying glass is actually a convex lens, and the magnification is limited, so is C. The objective lens of a microscope turns the object into an enlarged real image, and then the real image is enlarged through the eyepiece, so that the tiny object can be magnified many times and seen clearly. D is correct.

Answer: d

10 minute training (intensive training, which can be used in class)

1. The following statement about the use of telescopes is wrong ()

A. Telescopes are used to observe distant objects.

B. Telescopes have important military uses.

C. telescopes have important applications in astronomy.

Telescopes can be used to observe the structure of plant cells.

Thinking analysis: Telescopes are used to observe distant objects, which can make distant objects image in front of us. Telescopes are used to observe the enemy's situation, study the enemy's military position, and so on. Astronomy is used to observe celestial bodies, especially for the study of astrology. Telescopes cannot be used to observe the structure of plant cells. Option d is wrong.

Answer: d

2. The following statement about microscope is true ()

A. the magnification of electron microscope is higher than that of optical microscope.

B. When the indoor light is dark, use the concave surface of the reflector.

The magnification of a microscope is equal to the sum of the magnifications of the objective lens and the eyepiece.

D. The objective lens and eyepiece of the microscope are magnified virtual images.

Thinking analysis: the magnification of optical microscope is usually between several hundred times and several thousand times, and that of electron microscope is much larger. Tunneling scanning microscope can help us see the outline of molecules and atoms clearly, and A is correct. The reflector has two reflecting surfaces, one is a flat mirror and the other is a concave mirror. Both of them are used to reflect some light and increase the brightness of objects through slides. Concave mirror can converge light, which makes the light passing through the glass slide stronger. Therefore, when the indoor light is dark, the concave surface of the reflector should be used. B is right. The magnification of microscope is equal to the product of the magnification of objective lens and eyepiece, and option C is wrong. The objective lens of the microscope is an enlarged real image and the eyepiece is an enlarged virtual image, so option D is wrong.

Answer: AB

3. The following statement about telescope is incorrect ()

A. All telescopes are composed of two convex lenses.

B the larger the diameter of the telescope objective, the easier it is to observe the darker planets.

C. We see that cars in the distance are getting smaller and smaller, because the perspective of cars on us is gradually decreasing.

D. the objective lens of the telescope becomes a reduced real image.

Analysis of ideas: the objective lens and eyepiece of Kepler telescope are convex lenses; Galileo telescope's objective lens is a convex lens, and the eyepiece is a concave lens. Newton's "reflective telescope" has a concave mirror as the objective lens and a convex lens as the eyepiece, so option A is wrong. The larger the diameter of the telescope's objective lens, the more light it gathers and the brighter the image it forms, so option B is correct. For the same object, the smaller the angle of view to the human eye, the smaller the object we see, and item C is correct. The objective lens of the telescope becomes a reduced real image, and the eyepiece becomes an enlarged virtual image. D is correct.

A: A.

4. A telescope is also composed of two groups of convex lenses. Those close to the observed object are called objective lenses, and those close to the eyes are called eyepieces. The role of the objective lens is similar to ().

A. Projector B. Magnifier C. Camera D. Slide projector

Ideological analysis: the objective lens is used to make the distant object become an inverted and reduced real image near the focus, so the objective lens acts like a camera.

Answer: c

5.(20 10 Simulation of Shiyan Curriculum Reform Area in Hubei Province) One of the following optical knowledge applications is different from the other three, and this application is ().

A. astronomers observe celestial bodies through telescopes.

B. The actors practice dancing in front of the mirror.

Doctors use concave lenses to correct myopia.

D. Photographers take pictures with cameras

Train of thought analysis: From the four options, it is not difficult to find that items A, C and D apply the knowledge of light refraction, while item B applies the reflection of light, so choose B.

Answer: b

Happy time

metal and stone―hardness and strength

The middle school entrance examination is coming, and the students are very busy.

In order to encourage everyone, the teacher said, "Students, work harder and get in. If in ancient times, everyone was a scholar. " When the words were spoken, most people in the classroom looked up and pointed at their glasses and replied, "Teacher, we have long been nearsighted!" " "

30-minute training (consolidation training can be used after class)

1. Microscopes can magnify tiny objects at high magnification. It uses two convex lenses with different focal lengths as eyepiece and objective lens respectively, so the image formed by objective lens and eyepiece is ().

A. the objective lens is inverted to enlarge the real image.

B. Both the objective lens and the eyepiece are real images.

C. Both the objective lens and the eyepiece are virtual images.

D, the eyepiece becomes a vertical magnified virtual image.

Thinking analysis: The imaging principle of the microscope is that the observed tiny object is between the focal length of the objective lens 1 and the focal length of the objective lens1and the focal length of the objective lens1and becomes an inverted magnified real image, which is located in the focal point of the eyepiece and becomes an upright magnified virtual image. So a and d are correct.

Answer: AD

2. When observing an object with a microscope and telescope, the following statement about inverted image is correct ()

A. When observed with a microscope, it looks upright, and when observed with an astronomical telescope, it looks upside down.

B. when observed with a microscope, it looks positive, and when observed with an astronomical telescope, it looks positive.

C. It looks upside down when observed with a microscope, and it looks upright when observed with an astronomical telescope.

D. The image looks upside down when observed with a microscope and upside down when observed with an astronomical telescope.

Thinking analysis: the objective lens of microscope and astronomical telescope is an inverted real image, which passes through their respective eyepieces and becomes an upright magnified virtual image. They all go through an inverted image, a positive image and two imaging results, so that people can finally observe the inverted image. However, what we get through the microscope is the enlarged image of the object after inversion, and what we get through the astronomical telescope is the inverted image of the object after reduction.

Answer: d

3. The diameter of the objective lens of Hubble telescope is 4.3 m (the aperture of its optical primary mirror is 2.4 m). The reason for making such a large objective lens is ().

A. The bigger the objective lens, the bigger the image we see.

B reflecting telescope's objective lens should be larger than that of a refracting telescope.

The larger the objective lens is, the more light is collected and the brighter the image is.

D. All the above statements are wrong.

Thinking analysis: In order to let the telescope see the dark objects in the distance, we must find ways to gather more light and make the image brighter. The practical way to achieve this goal is to make the diameter of the telescope objective much larger than the pupil of our eyes.

Answer: c

4. It can be seen from the light path diagram in the microscope structure diagram ()

A. The focal length of the eyepiece is relatively long, and the focal length of the objective lens is relatively short.

B The focal length of the eyepiece is relatively short, and the focal length of the objective lens is relatively long.

The focal lengths of the eyepiece and the objective lens are the same.

D there is no clear requirement for the focal length of eyepiece and objective lens.

Thinking analysis: As shown on the right, the focal length of the objective lens is smaller than the distance from the slide to the lens. Because the image formed by the objective lens is within the focal length of the eyepiece, the focal length of the eyepiece is greater than the distance from the real image to the eyepiece, so the focal length of the eyepiece is longer and the focal length of the objective lens is shorter. Therefore, A is correct.

A: A.

5. The following statement is incorrect ()

A. The microscope consists of two convex lenses, the eyepiece is an inverted magnified real image, and the objective lens is an upright magnified virtual image.

B. Telescopes are divided into refractive telescopes and reflecting telescope.

Microscopes, telescopes and eyepieces are all virtual images.

D No matter what kind of telescope, the larger the diameter of the objective lens, the better.

Thinking analysis: The objective lens of microscope is a real image with inverted magnification, and the eyepiece is a virtual image with vertical magnification, so A is incorrect. Whether it is a microscope or a telescope, the eyepiece is an upright and magnified virtual image. The larger the diameter of the objective lens of various telescopes, the more light collected and the clearer the observation.

A: A.

6. When Yang Li observed epithelial cells with a microscope, through adjustment, the observed object was already in the center of the field of vision, but the image was too small to be observed clearly, so it should be ().

A keep the objective lens away from the object and keep the eyepiece position unchanged.

B keep the objective lens close to the object and the eyepiece away from the objective lens.

Keep the objective away from the object and the eyepiece close to the objective.

D keep the position of the objective lens unchanged and keep the eyepiece closer to the objective lens.

Thinking analysis: magnifying an object into a real image through a microscope. If you want to make the image bigger, you should put the object close to the objective lens. At this time, the image becomes larger and the image distance becomes larger, which makes the distance between the real image and the eyepiece smaller, so the eyepiece should be far away from the objective lens. So you should choose B.

Answer: b

7. There are many cheap toy telescopes in the market. Several students cooperated to buy one and came back to explore together.

(1) First put the eyepiece in front of you to observe the scene in front of you, then turn the telescope around and put the objective lens in front of you to observe the scene in front of you. Have you observed the same scenery twice? Write down the differences.

Eye observation eyepiece: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Eye observation target: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(2) Take the telescope apart, carefully observe its structure, draw a structural diagram, reassemble it, try to analyze the shortcomings of the toy telescope, put forward suggestions for improvement, and communicate with several students to record the results of the communication.

Ideological analysis: the toy telescope consists of two convex lenses. Because the focal length of the objective lens is larger than the focal length of the eyepiece, the eye sees the magnified image of the object when observing the eyepiece, and the image of the object becomes smaller and farther when observing the objective lens.

Answer: (1) Eye observation eyepiece: make the object bigger and closer; Eye observation objective; Make objects smaller and farther away. (2) Omission

8. Take two magnifying glasses with different focal lengths, one in each hand, and look at the object in front through two lenses, as shown in Figure 3-5- 1, and adjust the distance between the two magnifying glasses until you can see clearly. Is the object getting bigger or smaller? Switch the positions of the two magnifying glasses back and forth. What did you find? Why use two magnifying glasses with different focal lengths?

Figure 3-5- 1

Thinking analysis: This topic demonstrates the imaging principle of the telescope through two magnifying glasses with different focal lengths. The convex lens in front is equivalent to the objective lens of the telescope, which makes the distant object become a real image near the focus, and the convex lens in the back is equivalent to the eyepiece of the telescope, which is used to enlarge this real image, so what we see is the enlarged image of the object. If the positions of the front and rear convex lenses are reversed, a reduced image of the object can be seen. Through experiments, it is found that in order to see the magnified image of the object, the focal length of the objective lens should be long and the focal length of the eyepiece should be short.

Answer: As the object gets bigger, switching back and forth becomes smaller. Therefore, only when the focal length of the objective lens is long and the focal length of the eyepiece is short can we see that the distant object becomes larger. If the focal lengths of the two lenses are equal, the objects you see are about the same size, so they can't function as a telescope.

9. As shown in Figure 3-5-2, the visual angle of the object to the eye determines the size of the object imaging on the retina. The larger the viewing angle, the larger the image, and the clearer the eyes see the object. The viewing angle is not only related to the size of the object, but also related to the distance from the object to the eye. Can you explain that tiny objects can be seen clearly with a microscope and distant objects can be seen clearly with a telescope according to the knowledge of visual angle? In addition, the image formed by the plane mirror is the same size as the object, but why do people see their image in the plane mirror in the distance, but when they approach the plane mirror, they see a big image?

Figure 3-5-2

Answer: According to the function of microscope objective and eyepiece, both mirrors can enlarge the object, thus increasing the viewing angle, increasing the magnification and seeing the tiny object clearly. The objective lens of the telescope makes the image of a distant object close to the focus and the human eye, which is equivalent to shortening the distance from the object to the eye, thus increasing the viewing angle. Coupled with the magnifying effect of the eyepiece, the object is magnified again, and the viewing angle is increased, so that the distant object can be seen more clearly. When people look at their own images in different positions in the plane mirror, they are all "near big and far small", which is also caused by the perspective. When people look at their own image close to the flat mirror, it is equivalent to narrowing the distance from the image to the human eye, thus increasing the viewing angle and making the seen image bigger and clearer.