41.
2ax2-3x + 2ax-3 = .
42.
9x2-66x + 121 = .
43. factorize 8-2x2 = .
44. factorize x2-x + 14 = .
45. factorize 9x2 - 30x + 25 = .
46. factorize -20x2 + 9x + 20 = .
47. factorize 12x2 - 29x + 15 = .
48. factorize 36x2 + 39x + 9 = .
49. factorize 21x2 - 31x - 22 = .
50. factorize 9x4 - 35x2 - 4 = .
51. factorize (2x + 1)(x + 1) + (2x + 1)(x - 3) = .
52. factorize 2ax2-3x + 2ax-3 = .
53. factorize x(y + 2) - x - y - 1 = .
54. factorize (x2 - 3x) + (x - 3)2 = .
55. factorize 9x2-66x + 121 = .
56. factorize 8-2x2 = .
57. factorize x4-1 = .
58. factorize x2 + 4x - xy - 2y + 4 = .
59. factorize 4x2 - 12x + 5 = .
60. factorize 21x2 - 31x - 22 = .
61. factorize 4x2 + 4xy + y2 - 4x - 2y - 3 = .
62. factorize 9x5 - 35x3 - 4x = .
63.Factorize the following equations:
(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) = .
(7) 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)2x2 + ax-6x-3a = .
(4) 22x2-31x-21 = .
70.Factorize 3ax2 - 6ax = .
71. factorize (x + 1)x - 5x = .
72. factorize (2x + 1)(x - 3) - (2x + 1)(x - 5) =
73. factorize xy + 2x - 5y - 10 =
74. factorize 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 + 121
17. Factorization
(1) 8x2-18 (2) x2-(a -b)x-ab
18. Factorize the following equations
(1)9x4 + 35x2-4 (2)x2-y2-2yz- z2
(3)a(b2-c2)-c(a2-b2)
19. Factorize (2x+1)(x+1) + (2x+1)(x-3)
20. 39x2-38x + 8
21. Use factorization to find the value of (6512 )2-(3412 )2
22. Factorize a(b2 - c2) - c(a2 -b2)
24. Factorize 7(x-1)2 + 4(x-1)(y + 2) - 20(y + 2)2
25. Factorize xy2-2xy -3x-y2-2y-1
26. factorize 4x2-6ax + 18a2
27. factorize 20a3bc- 9a2b2c-20ab3c
28. factorize 2ax2 - 5x + 2ax - 5
29. factorize 4x3 + 4x2 - 25x - 25
30. factorization (1 - xy)2 - (y - x)2
31. factorization
(1)mx2 - m2-x + 1 (2)a2 -2ab + b2-1
32. Factorize each of the following
(1)5x2-45 (2)81x3-9x (3)x2-y2 -5x-5y (4)x2-y2 + 2yz-z2
33. Factorize: xy2-2xy-3x -y2-2y-1
34. Factorization y2(x-y) + z2(y-x)
1)Factorization x2 + x + y2- y-2xy =
35. factorize x2 - 25 = .
36. factorize x2 - 20x + 100 = .
37. factorize x2 + 4x + 3 = .
38. factorize 4x2 - 12x + 5 = .
39. Factorize the following equations:
(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)
Explanation:(ab+b)2?(a+b)2 = (ab+b+a+b)(ab+b?a?b) = (ab+2b+a)(ab?a) = a(b?1)(ab+2b+a).
(2) Answer: (x?a)4
Explanation: (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
Explanation: original equation = 7xn?1 ?x2?7xn?1 ?2x+7xn?1 = 7xn?1(x2 ____________ lens imaging, the eyepiece acts like a ____________, again to this image into a magnified ____________ (fill in the "real" or "virtual") image.
Thinking analysis: microscope imaging principle tells us that the object through the objective lens into an inverted magnified solid image, this solid image in the eyepiece within the focus, and then through the eyepiece into an orthogonal magnified virtual image, the objective lens imaging and the same as the lens of the camera, the role of the eyepiece like a magnifying glass.
Answer: real camera magnifying mirror false
2. (2010 Guiyang, Guizhou, simulation) If you want to look closely at the internal structure of a leaf, it is best to use ( )
A. plane mirror B. concave lens C. magnifying glass D. microscope
Thinking solution: the plane mirror into the same size of the false image, do not play the role of magnification, A wrong. A concave lens does not magnify objects, B is also wrong. A magnifying glass is actually a convex lens, and the magnification is also limited, C is also wrong. The objective lens of a microscope makes a magnified image of the object, and then the eyepiece is used to magnify the image so that it can be enlarged many times and very small objects can be seen, D is correct.
Answer: D
10 Minute Training (Intensive Training, can be used in class)
1.The following statements about the use of telescopes are incorrect ( )
A. Telescopes are used to look at objects at a distance
B. Telescopes have an important military application
C. Telescopes have a very important astronomical applications
D. Telescopes can be used to observe the structure of plant cells
Idea Analysis: Telescopes are used to observe objects at a distance, and they can make objects that are very far away be imaged in front of the eye. Telescopes are used in the military to observe the enemy, study enemy positions and so on have very important applications. In astronomy, it is used to observe celestial bodies, especially for the study of stars, which has made great contributions. Telescopes cannot be used to observe the structure of plant cells. The statement in option D is wrong.
Answer:D
2. The following statements about microscopes are correct ( )
A. An electron microscope has a higher magnification than an optical microscope
B. When the light in the room is dim, the concave side of the reflector is used
C. The magnification of a microscope is equal to the sum of the magnification of the objective lens and eyepiece
D. The objective and eyepiece of a microscope make a magnified virtual image
Idea Analysis: The magnification of an optical microscope is usually between a few hundred and a few thousand times, and the magnification of an electron microscope is much greater.Tunneling and scanning microscopes help us to see the outlines of molecules and atoms.A is correct. A reflector has two reflective surfaces, a flat mirror and a concave mirror, both of which are designed to reflect some of the light through the carrier sheet to increase the brightness of the object, and the concave mirror has a converging effect on the light so that the light through the carrier sheet is stronger, so the concave side of the reflector is used when the light in the room is dim, B is correct. The magnification of a microscope is equal to the product of the magnification of the objective lens and the eyepiece, option C is wrong. The objective lens of a microscope forms a magnified solid image and the eyepiece forms a magnified virtual image, so option D is wrong.
Answer:AB
3.The following statements about telescopes are incorrect ( )
A.All telescopes are made of two convex lenses
B.The larger the diameter of the objective lens of a telescope, the easier it is to observe fainter planets
C.The reason that we see cars in the distance getting smaller and smaller is that the angle of view they have on us is D. The objective lens of a telescope makes a reduced solid image
Ideas: The objective and eyepiece of the Kepler telescope are convex lenses; the objective lens of the Galilean telescope is a convex lens and the eyepiece is a concave lens; the reflecting telescope designed by Isaac Newton is a convex telescope and the eyepiece is a concave telescope. Newton's "reflecting telescope" has a concave objective lens and a convex eyepiece. So option A is wrong. The larger the diameter of the telescope's objective lens, the more light will converge and the brighter the image will be, so option B is correct. For the same object, the smaller its angle of view to the human eye, the smaller we see the object, C is correct. The objective lens of a telescope forms a reduced solid image and the eyepiece forms a magnified virtual image, D is correct.
Answer:A
4. There is a type of telescope that also consists of two sets of convex lenses. The one near the object to be observed is called the objective lens, and the one near the eye is called the eyepiece. The objective lens acts as if it were a ( )
A. Projector B. Magnifying glass C. Camera D. Slide projector
Thinking Analysis: The objective lens is used to make an inverted, reduced, solid image of a distant object near the focal point, so the objective lens acts as if it were a camera.
Answer: C
5.(2010 Hubei Shiyan classroom reform district simulation) One of the following applications of optics is different from the other three, and this application is ( )
A. Astronomy enthusiasts use telescopes to observe celestial bodies
B. Actors practice their dance moves in mirrors
C. Doctors use a concave lens to correct the vision of a patient suffering from myopic vision
D.Photographers use cameras to take pictures
Idea Analysis: It is not difficult to find out from the four options that A, C and D apply the knowledge of refraction of light, while B applies the reflection of light, so choose B.
Answer: B
Happy Hour
Progressions
With the promotion exams coming soon, the students are busy not having a good time.
The teacher, in order to encourage everyone, said, "Students, try harder, and if you pass the exam, you can be considered a Jinshi if you were in the ancient times." As soon as the words came out of his mouth, the vast majority of the classroom looked up, pointed at their glasses, and replied, "Teacher, we've been myopic for a long time!"
30-minute training (consolidation class training, can be used after class)
1.Microscope can be a high magnification of tiny objects, it uses two convex lenses with different focal lengths as the eyepiece and the objective lens, then the objective lens and the eyepiece formed by the image of ( )
A. Objective lens into an inverted magnification of the real image
B. Objective lens and eyepiece are formed by the solid image
B. p>C. Both the objective lens and the eyepiece form an imaginary image
D. The eyepiece forms an orthogonally magnified imaginary image
Idea Analysis: The imaging principle of a microscope is that the tiny object being observed between the 1x and 2x focal lengths of the objective lens forms an inverted and magnified solid image, and the image is located within the focus of the eyepiece, which is an orthogonally magnified imaginary image. Therefore, A and D are correct.
Answer: AD
2. When an object is observed with a microscope and a telescope, the following statements are correct about the inversion of the image ( ）
A. The image is upright when observed with a microscope and inverted when observed with an astronomical telescope
B. The image is upright when observed with a microscope and upright when observed with an astronomical telescope
C. The image is upright when observed with a microscope and inverted when observed with an astronomical telescope
B. The image is upright when observed with an astronomical telescope
B. The image is upright when observed with an astronomical telescope. p>C. The image is inverted when viewed through a microscope and upright when viewed through an astronomical telescope
D. The image is inverted when viewed through a microscope and inverted when viewed through an astronomical telescope
Idea Analysis: The objective lenses of the microscope and astronomical telescope both make an inverted solid image, which then passes through their eyepieces and forms an orthogonally magnified virtual image. They are respectively after an inverted image, and then after an orthogonal image, the result of two imaging, so that people ultimately observed are inverted image. But through a microscope one gets an inverted magnified image of the object, and through an astronomical telescope one gets an inverted reduced image of the object.
Answer: D
3. The Hubble telescope has an objective lens of 4.3 m in diameter (the aperture of its optical primary mirror is 2.4 m), and the reason for making such a large objective lens is that ( )
A. the larger the objective lens, the larger the image we can see
B. a reflecting telescope's objective should be larger than a refracting telescope's objective lens
C. the larger the objective, the more light it will converge. C. The larger the objective lens, the more light will be converged to make the image brighter
D. All of the above statements are wrong
Idea: In order to make the telescope to see the darker objects in the distance, we need to find a way to converge more light, so that the resulting image is a little brighter to achieve the purpose of a practical approach is to telescope the diameter of the objective lens is much bigger than the pupil of our eyes.
Answer: C
4. From the diagram of the structure of the microscope, the optical path can be seen ( )
A. The focal length of the eyepiece is longer, and that of the objective lens is shorter
B. The eyepiece is shorter, and that of the objective lens is longer
C. The eyepieces and the objectives are as long as each other
D. There is no clear requirement for the lengths of the eyepieces and objective lens. There is no clear requirement for the length of the eyepiece and the focal length of the objective lens
Idea Analysis: As shown in the figure on the right, the focal length of the objective lens is less than the distance from the carrier plate to the lens, and because the image formed by the objective lens is located within the focus 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.
Answer: A
5. The following statements are incorrect ( )
A. A microscope consists of two convex lenses, with the eyepiece forming an inverted magnified image and the objective lens forming an orthogonally magnified image
B. Telescopes are divided into refracting telescopes and reflecting telescopes
C. In microscopes and all forms of telescopes, the eyepieces form an image of an imaginary image
D. In telescopes and other forms of telescopes, the eyepieces form an imaginary image
D. p>
D. No matter what form of telescope, the larger the diameter of the objective lens, the better
Thinking analysis: microscope objective lens into an inverted magnified real image, the eyepiece into an upright magnified virtual image, so A is not correct. Both microscopes and telescopes, the eyepiece into a positively magnified virtual image. The larger the diameter of the objective lens of various telescopes, the more light is collected and the clearer the observation.
Answer: A
6. When Li Yang was observing epithelial cells with a microscope, he adjusted it so that the object being observed was in the center of the field of view, but the image was too small to be observed clearly, so he should ( )
A. move the objective lens away from the object, and keep the eyepiece in the same position
B. move the objective lens closer to the object, and the eyepiece farther away from the objective lens
C. move the objective lens closer to the object, and keep the eyepiece farther away from the objective lens. C. keep the objective lens away from the object, the eyepiece closer to the objective lens some
D. make the position of the objective lens is unchanged, the eyepiece closer to the objective lens some
Ideas: the object through the microscope into a magnified solid image, want to make the image bigger, we must put the object closer to the objective lens, then the image becomes bigger, at the same time the distance becomes bigger, so that the solid image from the eyepiece of the distance decreases, so the eyepiece should be away from the objective lens some.
Answer: B
7. There are a lot of very cheap toy telescopes on the market, several students cooperate to buy one back to explore together.
(1) First put the eyepiece in front of your eyes to observe the scene in front of you, then turn the telescope around and put the objective lens in front of your eyes to observe the scene in front of you. Do you observe the same scene both times? Write the difference.
The eye observes the eyepiece: ____________________________________________________________
The eye observes the objective lens: ____________________________________________________________
(2)Disassemble the telescope and observe its construction carefully, draw the structure diagram, then assemble it, try to analyze the shortcomings of the toy telescope, put forward the opinions of improvement, a few students exchange ideas, and exchange the The results are recorded.
Thinking analysis: the toy telescope is composed of two convex lenses, because the focal length of the objective lens is larger than the focal length of the eyepiece, so the eye observes the eyepiece to see the magnified image of the object, the eye observes the objective lens to see the object's image of the shrinking, and farther away.
Answer:(1)The eye observes the eyepiece: it makes the object larger and closer; the eye observes the objective lens; it makes the object smaller and farther away. (2)Slightly
8. Take two magnifying glasses with different focal lengths, hold one in one hand, and look at the object in front of you through the two lenses, as shown in Figure 3-5-1, and adjust the distance between the two magnifying glasses until you see it most clearly. Has the object gotten bigger or smaller? What do you discover when you adjust the positions of the two magnifying lenses back and forth? Why did you use two magnifiers with different focal lengths?
Figure 3-5-1
Idea Analysis: This question demonstrates the principle of telescope imaging through two magnifying lenses with different focal lengths, the convex lens in front of the telescope is equivalent to the objective lens, so that the object in the distance near the focus of the image, the convex lens behind the telescope is equivalent to the eyepiece, which is used to magnify the image, so we see a magnified image of the object. If the position of the two convex lenses before and after the reversal of the position of the object to see a reduced image. Through the experiment, it was found that to see a magnified image of the object, the focal length of the objective lens is required to be long and the focal length of the eyepiece is required to be short.
Answer: the object becomes larger, the front and back are reversed, the object becomes smaller, so only when the focal length of the objective lens is long and the focal length of the eyepiece is short we can see the object in the distance becomes larger. If the focal lengths of the two lenses are equal, the size of the object seen is almost the same, and the telescope does not work as a telescope.
9. As shown in Figure 3-5-2, the angle of view of an object to the eye determines the size of the image of the object on the retina, the larger the angle of view, the larger the image, the clearer the eye to see the object. Angle of view 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, based on the knowledge of the angle of view, the reasoning behind the ability to see tiny objects with a microscope and distant objects with a telescope? Also, the image made by a plane mirror is equal in size to the object, but why is it that a person sees a small image of himself in a plane mirror at a distance, but a large image when he approaches the mirror?
Figure 3-5-2
Answer: Based on the roles of the objective and eyepieces of a microscope, it can be seen that both mirrors act to magnify the object, thereby increasing the angle of view, allowing for higher magnification and clearer vision of tiny objects. The objective lens of the telescope makes the image of the distant object near the focal point, close to the human eye, which is equivalent to the distance from the object to the eye, thus increasing the angle of view, coupled with the magnifying effect of the eyepiece, once again enlarging the object, increasing the angle of view, so that you can see the distant object. People in the plane mirror to see their own near and far different positions of the image of the "near big far small", is also due to the perspective of the reason, people close to the plane mirror, look at their own image is equivalent to reduce the distance to the human eye, thus increasing the perspective, see the image becomes larger, also become clear.