Solve a mathematical problem; (XY-1) ^ 2 + (x + Y-2) (x + y-2xy) factorization

Solve a mathematical problem; (XY-1) ^ 2 + (x + Y-2) (x + y-2xy) factorization

(xy-1)^2+(x+y-2)(x+y-2xy)
=(xy-1)^2+(x+y)^2-2(xy+1)(x+y)+4xy
=(xy+1)^2+(x+y)^2-2(xy+1)(x+y)
=[（xy+1)-(x+y）]^2
=(1-x)^2(1-y)^2

As shown in the figure, there are two points P1 (x1, Y1) and P2 (X2, Y2) on the image of hyperbola y = KX (K ＞ 0, X ＞ 0), and x1 ＜ x2. Make a vertical line through P1 and P2 to the x-axis respectively, and the vertical feet are B and D. make a vertical line through P1 and P2 to the y-axis, and the vertical feet are a and C. (1) if you remember that the surface integrals of quadrilateral ap1bo and quadrilateral cp2do are S1 and S2 respectively, and the perimeter is C1 and C2, try to compare the sizes of S1 and S2, C1 and C2; (2) if p Is a point on the image of hyperbola y = KX (K ＞ 0, X ＞ 0), respectively passing through the x-axis and y-axis perpendicular lines in P direction, and the perpendicular feet are m and N. when the point P falls where, the perimeter of the quadrilateral PMON is the smallest?

(1) According to the geometric meaning of inverse proportional function coefficient K, S1 = S2 = k; when y1-y2 = x2-x1, that is, AC = BD, C1 = C2; when y1-y2 ＜ x2-x1, that is, AC ＜ BD, C1 ＜ C2; when y1-y2 ＞ x2-x1, that is, AC ＞ BD, C1 ＞ C2. (2) let P (x, y), that is, (x, KX), the perimeter of quadrilateral PMON =

For any two points P1 (x1, Y1) and P2 (X2, Y2) in the plane rectangular coordinate system, we call | x1-x2 | + | y1-y2 | the rectangular distance between P1 and P2
D (P1, P2)
1. Given that O is the origin of the coordinate and the moving point P (x, y) satisfies D (O, P) = 1, please write the relation between X and y
2. Let P0 (x0, Y0) be a certain point and Q (x, y) be a moving point on the straight line y = ax + B. we call the minimum value of D (P0, q) the straight line distance from P0 to the straight line y = ax + B, and try to find the right angle distance from m (2,1) to the straight line y = x + 2

(1) It is shown in the figure that (2) ∵ D (m, q) = | X-2 | + | Y-1 | = | X-2 | + | x + 2-1 | = | X-2 | + | x + 1 and ∵ x can take all real numbers, and | X-2 | + | x + 1 | represents the sum of the distances from the points corresponding to the real numbers x on the number axis to the points corresponding to the numbers 2 and - 1

1、-27m²n+9mn²-18mn
2、ab+a+b+1
3、（x-1）（x-2）-2（2-x）²

1.9mn(-3m+n-2)
2.(b+1)(a+1)
3.(x-2)(3-x)

In January 2012, Uncle Wang deposited some money in the bank for three years at an annual interest rate of 5.00%. After maturity, he could withdraw 92000 yuan. How much yuan did Uncle Wang deposit?

Sum of principal and interest = principal * (1 + annual interest rate * term)
Principal = sum of principal and interest / (1 + annual interest rate * term) = 92000 / (1 + 5% * 3) = 80000
So Uncle Wang deposited 80000 yuan

Definition of mathematical problem solving
What kind of diamond is a square? What's the difference between a square and a diamond?

A diamond with an angle of 90 degrees is a square
The difference is that the angle of a square is 90 degrees
The angle of the diamond is between 0 and 180

Today is Tuesday. What day is it in 100 days?

100 △ 7 = 14 (weeks) 2 (days); the remainder is 2. Two more days from Tuesday is Thursday. A: two more days is Thursday

Prepare 10 small cards with the number of 1 to 10 written on them. Then put the cards together and wash them well. Take out one at a time, then put them back and wash them well
When the number of experiments is 20, what is the frequency of the multiple of 3, what is the frequency, 40, 60, 80, 100, 140, 160

Every time the probability of the multiple of 3 is 0.3, the frequency of the multiple of 3 in 20 experiments is 20x0.3 = 6, and the frequency is 1 / 0.3 = 3.333. The frequency has nothing to do with the number of times of extraction. It is this number. As for the frequency of different times of extraction, it is 0.3x

Thinking question: 58 divided by 17 times 34 in a simple way

58 divided by 17 times 34
=58×34÷17
=58×2
=116

Quadratic equation of one variable
1. If a is the root of the equation x + BX + a = 0, and a is not equal to 0, then the value of a + B is?
2. It is known that one root of the quadratic equation of one variable x-kx + 1 = 0 is the root sign 2 + 1, and the value of K is obtained
3. Judge whether the square of the equation x-ax (2x-a + 1) = x is a quadratic equation of one variable, if so, point out the quadratic coefficient and the linear coefficient

1. A is the root of the equation about X. take x = a into the equation to get a ^ 2 + AB + a = 0, and the common factor A (a + B + 1) = 0. If a is not equal to 0, then the factor A + B + 1 = 0, then a + B = - 1
2. Take x = √ 2 + 1 into the equation to get (√ 2 + 1) ^ 2-k (√ 2 + 1) + 1 = 0, and sort out the equation to get k = 2 √ 2
3. According to the reduced power of the original equation, we can get (1-2a) x ^ 2 + (a ^ 2-a-1) x = 0, quadratic coefficient 1-2a, primary coefficient a ^ 2-a-1