I. Choose the underlined word or phrase (marked A, B, C or D) in each sentence that needs correcting. 1. My sister is very seriously and hard-working in her study. A B C D 2. Ride a bike at the weekend is my best friend's hobby. 3. She is very cared, so she always helps her mother do the housework. 4. My friend has a short brown hair and an oval face. 5. Because Nga is very keen on the school's singing competition, she is taking part on it tomorrow. 6. I have an important maths exam tomorrow afternoon, so I do a lot of maths exercises at home this evening. 7. We have a lot of assignments to do. Therefore, we are going to the cinema with you tonight. 8. I have new pencil, a pencil sharpener and a pencil case. 9. The painting competition will start at his school on the 17th of October. 10. She usually plays the piano every Monday evening, but today she watch cartoons with her younger sister. 11. There are a table, four chairs, two pictures and a vase in the living room. 12. There aren't a lot of posters in the wall in his bedroom. 13. My dog has a long tail, big eyes and a yellow fur. 14. She has a birthday party with a big birthday cake and a lot of candles at home at present. 15. She is short hair and big eyes 16. My new friend, Zoe, is very friend and helpful 17. Tomorrow, John and I is playing basketball with our team 18. This student are very smart, studious and well-behaved 19. My mother have an oval face and lovely smile 20. Would you like going to the movies tonight?

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Bài 1: Điền và chỗ (….) để được hằng đẳng thức đúng. a) ……. + 8xy + …….. = (…… + 4y2) b) ….. – …… + 25y2 = (2x – ……)2 c) 25x2 – 10xy + ……. = (……– …….)2 d) 16x2 + ….. + 49y2 = (….. + ….. )2 e) ….. + …… + …... + 27y3 = (2x + ……)3 g) ….. – …… + 12y2 –……. = (…..– 2y )3 Bài 2: Chỉ ra những chỗ sai của một trong hai vế và sửa lại cho đúng các hằng đẳng thức (sửa ít nhất). a) x2 – 2xy + 4y2 = (x – 2y)2 b) a2 + 24ab + b2 = (4a + 3b)2 c) 9x2 + 6xy + y2 = (3x – y)2 d) a3 – 8a2b + 6ab2 – 8b3 = (a – 2b)3 Bài 3 Tính nhanh: a) A = 2012 d) D = 20162 – 2015. 2017 b) B = 4982 e) c) C = 93. 107 g) G = 20162 – 20152 + 20142 – 20132 + 20122 – 20112+ 22 – 12 h) Cho M = 992 + 972 + 952 + … + 32 + 12 và N = 982 + 962 + 942 + … + 42 + 22 Tính giá trị của biểu thức M – N + 50. Bài 4: Hãy vận dụng hằng đẳng thức số 1 và số 2 để đưa các biểu thức sau về dạng bình phương của một nhị thức với một hằng số. a) x2 – x + 1 b) x2 + 3x + 4 c) x4 – 4x2 + 6 d) 2x2 + 6x – 15 e) x2 – 5x + 9 g) 3x2 – 12x + 20 Bài 5: Hãy đưa mỗi biểu thức sau về dạng tổng hoặc hiệu hai bình phương: a) x2 + 10x + 26 + y2 + 2y b) a2 – 6a + 5 – b2 – 4b c) x2 – 2xy + 2y2 + 2y + 1 d) 4x2 – 12x – y2 + 2y + 8 Bài 6: Hãy vận dụng hằng đẳng thức hiệu hai bình phương để thu gọn các tích sau: a) (x+y+z)(x+y –z) b) (x+y+z)(z–y+z) c) (x–y–z)(x+y+z) d) (x–y+z)(x+y–z) e) (a+b–c)(b+c–a) g) (b+c–a)(c+a–b) Bài 7: Hãy sử dụng hằng đẳng thức thu gọn các biểu thức sau: a) (a+b+c+d)(a+b–c–d) b) (a–b+c+d)(a–b–c–d) c) (x+2y+3z)(x+2y–3z) d) (x–4)(x2 + 16)(x+4) e) (x+y+4)(x+y–4) g) (x–y+6)(x+y–6) h) (a+2b–3)(a–2b–3) k) (x+2y+3z)(2y+3z–x) Bài 8: Rút gọn các biểu thức sau một cách nhanh nhất: A = (6x–2)2 + (2–5x)2 +2(6x–2)(2–5x) ; B = (2a2+2a+1)(2a2–2a+1) – (2a2 +1)2 C = (x+3)(x2–3x+9) – (54+x3) ; D = (2x+y)(4x2–2xy+y2)–(2x–y)(4x2+2xy+y2) E = (a+b)2 – (a–b)2 ; F = (a+b)3–(a–b)3–2b3