Fill in the missing words in the sentences below. Choose from the following:

at a loose end ; at death’s door ; at one’s wits’ end * (* change as appropriate) ; at a loss ; at fault ; at random ; at a pinch ; at first sight ; at shorts notice ; at a standstill ; at least ; at all costs ; at loggerheads ; at the crack of dawn ; at all hours ; at most ; at will ; at best ; at once ; at will

1. We must __________ catch the 7.30 train. Otherwise we won’t get to the meeting in time.

2. It is difficult to know who’s __________ in the matter. Perhaps we’re all to blame.

3. It’s late. I think you’d better go to bed now, darling. Remember, you’ve got to get up __________ tomorrow.

4. Since it’s his first offence he’ll probably get off with a warning - __________ a small fine.

5. If you’re __________ this weekend, Joan, why not come over for a meal? It’ll give us a chance to catch up on some gossip.

6. When her daughter didn’t come home on the last bus with the other girls, Mrs Jenkins was __________ - she was terrified that something dreadful had happened to her.

7. Like you, I’m __________ to explain the sudden fall in share prices. I’ve absolutely no idea what can have caused it.

8. Traffic was __________ this morning because of an accident of the A21.

9. I’m afraid everything’s __________ this week. Both the secretaries are ill and no one knows where anything is.

10. The hotel wasn’t that modern, but __________ it was cheap and reasonably clean.

11. I’ve got room in the car for three - four __________.

12. Mrs Smith’s daughter is terrible, isn’t she? Out __________ and never a kind word to anyone.

13. You should be able to sell your stereo equipment for £200 - __________ £250.

14. Of you don’t get out __________ then I shall have you thrown out.

15. Pamela and David are always __________. I really can’t imagine why they got married in the first place. They’ve got absolutely nothing in common.

16. A chameleon is a remarkable creature - it is able to change the colour of its skin __________.

17. You can’t expect me to work overtime __________ such __________! I need to be told at least two days in advance.

18. I was in a hurry for my train, so I choose a book __________.

Rút gọn biểu thức:

a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)

b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)

c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)

d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)

Cho \(\left(x+2y\right)\left(x^2-2xy+4y^2\right)=0\) và \(\left(x-2y\right)\left(x^2+2xy+4y^2\right)=16\). Tìm x và y

Cho x + y = a và xy = b. Tính giá trị biểu thức sau theo a; b

a) \(x^2+y^2\)

b) \(x^3+y^3\)

c) \(x^4+y^4\)

d) \(x^5+y^5\)

b) Cho \(x-y=1\), tính \(B=x^3-y^3-3xy\)

c) Cho \(x-y=2\), tính \(C=2\left(x^3-y^3\right)-3\left(x+y\right)^2\)

d) Cho \(a+b=1\), tính \(D=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)

Điền vào ... các hạng tử thích hợp:

a) \(\left(2a+..........\right)\left(..........-..........+..........\right)=8a^3+27b^3\)

b) \(\left(..........-..........\right)\left(25x^2+20xy+..........\right)=........-........\)