In junior high school, the principle of common factor is put forward, 1. Decomposition common factor: 2x (A-2) + 3Y (2-A) 2. The common factor of polynomial A & # 178; - 2Ab + B & # 178;, a & # 178; - B & # 178; is (?) 3. Given X & # 178; + X-1 = 0, find the value of the cubic power of X + 2x & # 178; + 1999

In junior high school, the principle of common factor is put forward, 1. Decomposition common factor: 2x (A-2) + 3Y (2-A) 2. The common factor of polynomial A & # 178; - 2Ab + B & # 178;, a & # 178; - B & # 178; is (?) 3. Given X & # 178; + X-1 = 0, find the value of the cubic power of X + 2x & # 178; + 1999

1.2X（a-2）-3y(a-2)=(2x-3y)(a-2)
2.a^2-2ab+b^2=(a-b)^2
a^2-b^2=(a+b)(a-b)
The common factor is (a-b)
3. From the known conditions, we can get x ^ 2 = 1-x, x ^ 2 + x = 1
X^3+2X^2+1999=X^3+2(1-X)+1999=X^3-2X+2001=X(X^2-2)+2001=X(X^2+X-X-2)+2001
=X(1-X-2)+2001=-(X^2+X)+2001=2000

Two questions about the method of quoting the common factor
1. Calculation: 1998 * 19991999-1999 * 19981998
2. Verification: if a three digit hundred digit number exchanges positions with each digit, then the difference between the new number and the original number can be divided by 99

1.1998*19991999-1999*19981998
=1998*1999*10001-1999*1998*10001
=0
2.100x+10y+z-(100z+10y+x)
=99x-99z

1. A businessman sells two goods at a time. One makes 15% and the other loses 15%. The selling price is 1955 yuan. How much did the businessman lose in this transaction?
2. A workshop received the task of processing x parts, planned to process 120 parts per day, which could be completed on schedule, while the actual processing of 40 parts per day, which was completed two days ahead of schedule
A series of equations are required

Let one be x and the other be y
x(1+15%)=1955
x=1700
y(1-15%)=1955
y=2300
Compensation of 1700 + 2300-1955 * 2 = 91 yuan
2.x/120-2=x/(120+40)
The solution can be obtained

After cutting a circular piece of paper, put it together into an approximate rectangle with the width equal to the radius and the area unchanged. The perimeter of the rectangle is 16.56 cm. What is the area of the cut circular piece of paper in square cm?

Let the radius of this circle be r. according to the meaning of the question, we can get: 2 × 3.14r + 2R = 16.56, & nbsp; & nbsp; 6.28r + 2R = 16.56, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 8.28r = 16.56, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; r = 2, 3.14 × 22, = 3.14 × 4, = 12.56 (square centimeter). Answer: the area of the paper is 12.56 square centimeter

Divide the figure into four figures of the same size and shape

According to the analysis, each square is divided into four small squares (as shown in the figure on the left), and then every three small squares form a figure, which can be divided into four figures of the same size and shape, as shown in the figure below

It took nine hours for a car to go from a to B and return to A. It took 100 kilometers an hour to go and 80 kilometers an hour to return. What's the distance between the two places
The solution is proportional,

Set the time to go to x hours and the time to return to 9-x hours
100x=80*(9-x)
100x=720-80x
180x=720
x=4
9-4 = 5 hours
Distance between the two places: 100x4 = 400km

On the mathematical formula of positive proportion in primary school
At least 20, the area and perimeter of the figure; three-dimensional figure and so on. It doesn't matter if you can't answer,

Y = ax, a > 0 or Y / x = a, X ≠ 0, but the range of X is different in the two cases

Sixth grade positive proportion and negative proportion exercises
The master and the apprentice cooperate in 84 parts. The master finishes one in 5 minutes and the apprentice finishes one in 9 minutes. How many parts do the master and the apprentice do?

At the same time, the master made x, and the apprentice made 84-x
The master made 1 / 5 in one minute, and the apprentice made 1 / 9 in one minute
The ratio of X to 84-x is 1 / 5 to 1 / 9
It is calculated that master x = 54, apprentice 84-x = 30

Inverse proportion error prone practice?

I have 1. The area of a circle is in direct proportion to its radius. 2. The area of a circle is in direct proportion to the square of its radius. 3. The area of a circle is in direct proportion to the square of its circumference. 4. The area of a square is in direct proportion to its side length

The application of equation in the formula of mathematical itinerary problem

The distance a takes + the distance b takes = the total distance
(the speed of a + the speed of B) x the time of meeting = the total distance
Go in the same direction (time x speed for a to catch up with B - time x speed for B = distance of a - distance of B)