Soon the end of the term, mathematics factorization is not good, up to now still a little do not understand. For example, decomposition a ^ 2 + 4AB + 4B ^ 2, I only know the result = (a + 2b) ^ 2, difficult to shout out, how to come out of the process? The book does not understand

Soon the end of the term, mathematics factorization is not good, up to now still a little do not understand. For example, decomposition a ^ 2 + 4AB + 4B ^ 2, I only know the result = (a + 2b) ^ 2, difficult to shout out, how to come out of the process? The book does not understand

A mathematical factorization problem
（-xy+1）（xy+1）（x²y²+1）
Write down the middle steps, OK? The process
（-xy+1）（xy+1）（x²y²+1）=（1-xy）（1+xy）(x²y²+1)=(x²y²+1)(x²y²+1)=1-(xy)4
1-x4y4
1-(xy)4
Given that x minus 3 is equal to 1 / 2 of X, find the square of x minus 3x plus 2
x-3=1/x
x（x-3）=1
x²-3x+2
=x（x-3）+2
=1+2
=3
Three
x-3=1/x
x²-3x+2
=x（x-3）+2
=xx1/x+2
=1+2
=3
If you want to do it with equations, it's better to be quadratic
1. 2. The length of train a and B are 144m and 180m, and train a runs 4m more per second than train B. (1) the two trains run in opposite directions, How many seconds does it take for the head of car a to catch up with the tail of car B and for the head of car a to overtake car B? 3. The distance between station a and station B is 488km. A slow train starts from station a and travels 60km per hour, while an express train starts from station B and travels 80km per hour, Q: (1) how many hours will the two trains meet each other when they leave at the same time? (2) when the two trains leave at the same time, the slow train starts for 28 minutes, and the fast train starts for how many hours will the two trains meet each other? (3) when the slow train starts at the same time, how many hours will the fast train catch up with the slow train after starting? 4. A train advances at a constant speed, from entering a 300 m long tunnel to completely passing through the tunnel for 20 seconds, A fixed lamp at the top of the tunnel shines on the train for 10 seconds. The length of the train body is 5. A train passes through a 500 m long tunnel at a constant speed. If the train takes 30 seconds from entering the tunnel to leaving the tunnel completely, and the time for the whole train to be completely in the tunnel is 20 seconds, the length of the train is calculated. 6, a and B trains are 200 meters and 280 meters respectively. They run at a constant speed on the double track, It is known that after 18 seconds, the speed ratio of car a and car B is 5:3. Find out the speed of the two cars. 7. If they walk around the 400m circular runway at the same time, they will meet for the first time in 2 minutes and 30 seconds; if they walk in the same direction from the same starting point, they will meet for the first time in 12 minutes and 30 seconds, 8. Xiao Zhang plans to go from home to the county. If he travels 20km per hour, he will be half an hour late. If he travels 25km per hour, he can arrive 12 minutes earlier. 9. For a job, a should do it 20 hours alone, B should do it 12 hours alone, now a should do it 4 hours alone, and the rest should be done by a and B together, How many more hours will it take? 10. A workshop processes a batch of parts within the planned time. If 40 parts are produced every day, 20 parts will be less and the task will not be completed. If 50 parts are produced every day, the task can be completed one day ahead of schedule and 10 parts will be more than that. How many parts are there and how many days are planned to be completed? 11. For a project, it takes 8 days for Party A to complete it alone, 12 days for Party B to complete it alone, and 24 days for Party C to complete it alone, Now three days after Party A and Party B work together, Party A leaves for business, and Party B and Party C work together. Ask Party B and Party C how many days it will take to complete the project. 12. Workshop a and workshop B produce the same kind of machines. Workshop a produces 80 machines a day, and workshop B produces 120 machines a day. If Party A produces for five days, then Party B starts production, How many days does it take for Party B to catch up with Party A's output? 13. A pool is equipped with three water inlet pipes (a, B and C). A single pipe can fill the pool in 45 minutes, a single pipe can fill the pool in 60 minutes, and a single pipe can fill the pool in 90 minutes. If the three pipes are opened together, how many minutes can the pool be filled. 14. Xinhua bookstore sells two kinds of books in one day, and a total of 1560 yuan is sold, In order to develop agricultural science and technology, type B books were sold in the countryside for a total of 1350 yuan. According to the cost of type a books and type B books, the profit of type a books is 25%, and the loss of type B books is 10%. How much is the total profit (or loss) of the bookstore this day? 15. It is understood that in the sales of individual clothing, as long as it is 20% higher than the purchase price, it can make a profit, but the boss often price it 50% - 100% higher than the purchase price, If you are going to buy a garment with a price of 200 yuan, within what range should you counter-offer? 17. An individual vendor sells two coats at the same time in a single sale. Each coat is sold at 135 yuan. According to the cost, one of them makes a profit of 25% and the other loses money of 25%. In this sale, do you make a profit or lose money, or do you not make a loss? (how many times will you make a profit,
1. The ship goes downstream from a to B for 9 hours, and returns to a for 11 hours. The speed of the ship in still water and the distance between a and B are calculated. Suppose the speed of the ship in still water is x km / h and the distance between a and B is y km
If the equation 3x & # 178; + MX = 2X-4 does not contain a linear term of X, then M =?
Move the term on the right to the left and see that M = 2
Please help me to solve the following three problems with the equation of degree 2
① Shunfeng tour group organized 200 people to huaguoling and yunshuidong. The number of people who went to huaguoling was twice as much as that to yunshuidong, one less. How many people went to both places?
② The distance between a and B is 6km. They start at the same time and walk in opposite directions. They meet in one hour. If they start at the same time and walk in the same direction, a can catch up with B in three hours. What is the average speed of the two?
③ One kind of royal jelly can be packed in two sizes, three large boxes and four small boxes with 108 bottles in total, two large boxes and three small boxes with 76 bottles in total?
1. X is the number of people in Yunshui cave, y is the number of people in huaguoling, 1) y = 2x-1, 2) x + y = 200, 1) substituting 2) x + 2x - 1 = 200, the solution is x = 37, y = 73, 37 people in Yunshui cave, 73 people in huaguoling, 2. The velocity of a is set to x, and the velocity of B is set to y x + y = 6; that is, 1) x = 6-y, 6 + 3Y = 3x, that is, 2) 2 + y = x1
Set Huaguo Mountain x, Yunshui cave y
There are 200 people in the tour group
x+y=200
The number of people in huaguoling is twice that in Yunshui cave, one less
x=2y-1
The solution is x = 133, y = 67
Let x, y respectively
Party A and Party B are facing each other, so the speed is added up, and they walk together for 6 hours
(x+y)*1=6
When a chases B and catches up with B, he walks 6 more
3x=3y+6
The solution is x = 4, y = 2
If the equation 2x & # 178; + MX = 3x + 2 does not contain a linear term, then what is m equal to
2x²+mx=3x+2
2x²+(m-3)x-2=0
∵ does not contain a single term
∴m-3=0
M=3
Finding the negative integer solution of the bivariate linear equation 2x + y + - 7
2x+7=-7
x=-1,y=-5
x=-2,y=-3
x=-3,y=-1
Just these three
The following equations are solved by factorization: (1) 16x2 = (X-2) 2; (2) 3x (x-1) = 2-2x; (3) (M + 2) (2m-5) = - 10
(1) 16x2 - (X-2) 2 = 0, (4x + X-2) (4x-x + 2) = 0, 4x + X-2 = 0 or 4x-x + 2 = 0, so X1 = 25, X2 = - 23; (2) 3x (x-1) + 2 (x-1) = 0, (x-1) (3x + 2) = 0, X-1 = 0 or 3x + 2 = 0, so X1 = 1, X2 = - 23; (3) 2m2-m = 0, m (2m-1) = 0, M = 0 or 2m-1 = 0, so M1 = 0, M2 = 12
Write out all the integer solutions of bivariate equation 4x plus y equal to 1
Y = 1-4x, when x is an integer, y must be an integer, so there are innumerable integer solutions