Factorization and quadratic equation of one variable 1、 Factorization 1.x^3-6x^2+12x-8；2.(x^2+y^2)-4x^2y^2；3.6x^2+7x+2；4.x^4-6x^2-8；5.x^2-(4a-1)+3a^2-a；6.ab-1+a-b；7.6x^n+1-14x^n+8x^n-1；8.(x^2+3x)^2-2(x^2+3x)-8；9.a^2+b^2-2ab-2b+2a+1；10.ax^2+3x-c=ax=x^2(a≠1)；11.abx^2-a^2x=b^2x-ab(ab≠0) 2、 Discriminant of the root of quadratic equation with one variable and Weida's theorem 1. By using the relationship between and coefficient, we can find the sum of squares and reciprocal of the quadratic equation 2x ^ 2 + 3x-1 = 0 2. The real roots of the equation x ^ 2-ax + B = 0 when a ^ 2 < 4B 3. Given the equation x ^ 2 + (2m + 1) x + (m-2) ^ 2 = 0 about X, what is the value of M (1) the equation has two real roots that do not want to be equal (2) the equation has two equal real roots (3) the equation has no real roots I know that I have a lot of questions and give few points. I can do one thing at a time, The tenth one is ax ^ 2 + 3x-2 = ax + x ^ 2 (a ≠ 1). Sorry to make a mistake

Factorization and quadratic equation of one variable 1、 Factorization 1.x^3-6x^2+12x-8；2.(x^2+y^2)-4x^2y^2；3.6x^2+7x+2；4.x^4-6x^2-8；5.x^2-(4a-1)+3a^2-a；6.ab-1+a-b；7.6x^n+1-14x^n+8x^n-1；8.(x^2+3x)^2-2(x^2+3x)-8；9.a^2+b^2-2ab-2b+2a+1；10.ax^2+3x-c=ax=x^2(a≠1)；11.abx^2-a^2x=b^2x-ab(ab≠0) 2、 Discriminant of the root of quadratic equation with one variable and Weida's theorem 1. By using the relationship between and coefficient, we can find the sum of squares and reciprocal of the quadratic equation 2x ^ 2 + 3x-1 = 0 2. The real roots of the equation x ^ 2-ax + B = 0 when a ^ 2 < 4B 3. Given the equation x ^ 2 + (2m + 1) x + (m-2) ^ 2 = 0 about X, what is the value of M (1) the equation has two real roots that do not want to be equal (2) the equation has two equal real roots (3) the equation has no real roots I know that I have a lot of questions and give few points. I can do one thing at a time, The tenth one is ax ^ 2 + 3x-2 = ax + x ^ 2 (a ≠ 1). Sorry to make a mistake

1.x^3-6x^2+12x-8； =(x-2)(x^2+x+4)-6(x-2) =(x-2)(x^2+x-2) 2.(x^2+y^2)^2-4x^2y^2； =x^4+2x^2y^2+y^4-4x^2y^2 =x^4++y^4-2x^2y^2 =(x^2-y^2)^2 3.6x^2+7x+2； =(2x+1)(3x+2) 4.x^4-6x^2+8； =(x^2-2)(x^2-4) =(x...

Three mathematical problems like factorization
-ab（2a-b）²+b（b-2a）²
-9m（m-n）-6m（n-m）²
81（x-y）²-16（x+y）²

Solution
-ab(2a-b)²+b(b-2a)²
=-ab(2a-b)²+b(2a-b)²
=(2a-b)(b-ab)
=b(2a-b)(1-a)
-9m(m-n)-6m(n-m)²
=9m(n-m)-6m(n-m)²
=3m(n-m)[3-2(n-m)]
=3m(n-m)(3-2n+2m)
81(x-y)²-16(x+y)²
=[9(x-y)+4(x+y)][9(x-y)-4(x+y)]
=(9x-9y+4x+4y)(9x-9y-4x-4y)
=(13x-5y)(5x-13y)

1)（x+1)(x+2)(x+3)(x+4)-120
2)(x^2+3x-3)(x^2+3x+4)-8
The main reason is that I haven't seen this type

1)
(x+1)(x+2)(x+3)(x+4)-120
=[(x+1)(x+4)][(x+2)(x+3)]-120
=(x^2+5x+4)(x^2+5x+6)-120
=(x^2+5x)^2+10(x^2+5x)+24-120
=(x^2+5x)^2+10(x^2+5x)-96
=[(x^2+5x)+16][(x^2+5x)-6]
=(x^2+5x+16)(x^2+5x-6)
=(x^2+5x+16)(x+6)(x-1)
2)
(x^2+3x-3)(x^2+3x+4）-8
=[(x^2+3x)-3][(x^2+3x)+4]-8
=(x^2+3x)^2+(x^2+3x)-12-8
=(x^2+3x)^2+(x^2+3x)-20
=(x^2+3x+5)(x^2+3x-4)
=(x^2+3x+5)(x+4)(x-1)

Equation or formula is OK, as long as you work it out, but don't be too troublesome. I can't understand. It's better to say why
The number of workers in workshop a is 36 more than that in workshop B. now 12 people are transferred from workshop a to workshop B. at this time, the number of workers in workshop B is 1 / 5 less than that in workshop A. how many people are there in workshop a?

If there are x people in workshop B, then there are x + 36 people in workshop a
According to the meaning of the title:
（x+36－12）×（1－1/5)=x
Because the number of people in workshop B is 1 / 5 less than that in workshop a, the number of people in workshop a multiplied by (1-1 / 5) is the number of people in workshop B
The solution is (x + 24) * 4 / 5 = X
4/5x+96/5=x
1/5x=96/5
x=96
There are 96-36 = 60 people in workshop B

We need it now
1. The bottom radius of a cylindrical container is 10cm, and the height is 20cm. The water depth in the container is 10cm. Now, immerse an object completely in the water, and the water depth becomes 15cm. Calculate the volume of the object
2. There is a cylindrical water cup with an inner diameter of 8cm, in which there is 15cm deep water, which just accounts for 80% of the volume of the water cup. What is the volume of the water cup?
3. Stack three cylindrical boxes with equal height and bottom radius of 10 cm together. If you take away one box, the surface area will be reduced by 314 square cm. What is the volume of each box?

1. The bottom radius of a cylindrical container is 10cm, and the height is 20cm. The water depth in the container is 10cm. Now, immerse an object completely in the water, and the water depth becomes 15cm. Calculate the volume of the object
3.14×10×10×（15-10）
=3.14×100×5
=1570 CC
2. There is a cylindrical water cup with an inner diameter of 8cm, in which there is 15cm deep water, which just accounts for 80% of the volume of the water cup. What is the volume of the water cup?
3.14×8/2×8/2×15÷80%
=3.14×16×15÷80%
=753.6÷80%
=942 CC
3. Stack three cylindrical boxes with equal height and bottom radius of 10 cm together. If you take away one box, the surface area will be reduced by 314 square cm. What is the volume of each box?
The height of each box is:
314÷（3.14×10×2）
=314÷62.8
=5 cm
The volume is 3.14 × 10 × 10 × 5 = 1570 cubic centimeter

At present, there are two engineering teams (team a and team B) to repair the river. The number of team a is five-thirds of that of team B. due to the need of work, 90 people are transferred from team a to team B. at this time, the ratio of team a to team B is 2:3. How many people are there in team a and team B?

If the number of team B is x, the number of team a is 5 / 3x
Then we get the formula:
（5/3x—90）：（X+90）=2：3
X = 150
Then there are 250 people in team a and 150 people in team B
Applause

A person from a to B, the first day of the whole journey 1 / 2, more than 16km, the second day of the journey is 7 / 8 of the first day, at this time there is 15km away from B, find the distance between a and B

Analysis: regard the distance between a and B as unit "1"“
The next day's journey is 7 / 16 (7 / 8 of 1 / 2) plus 14 km (7 / 8 of 16),
The sum of 15 + 16 + 14 is 1-1 / 2-7 / 16,
A and B = (15 + 16 + 16 × 7 / 8) / (1-1 / 2-1 / 2 × 7 / 8)
=45÷1/16
=720 km
Equation: let the distance between a and B be x km,
（1/2）x+16+（1/2）x×7/8+16×7/8+15=x,
（1/2）x+16+（7/16）x+14+15=x,
x-（1/2）x-（7/16）x=16+14+15
（1/16）x=45,
x=720.

If you want to make an equation, you can also make an equation
One day, the cinema sold 1700 tickets of type A and type B, with a total income of 780 yuan. Each ticket of type A is 60 cents, and each ticket of type B is 40 cents. How many tickets of type A and type B are sold?

Suppose there are x class a tickets, then there are 1700-x class B tickets
0.6x+0.4×（1700－x）＝780
0.6x＋680－0.4x＝780
0.2x＝100
x＝500
1700-500 = 1200 (sheets)
A: there are 500 class a tickets and 1200 class B tickets

A and B set out from the East and West stations at the same time, facing each other. After meeting, they moved forward at the same speed, and returned immediately after arriving at the other's place of departure. On the way, they met again. It is known that car a travels 40 kilometers per hour, 8 kilometers more than car B per hour, and the location of the two encounters is 80 kilometers. Find the distance between the East and West stations

The first time, the two cars traveled a whole journey, from the first encounter to the second encounter, the two cars traveled two whole journey
Suppose the distance between the two stations is s km, the time from the beginning to the first encounter is t hours, and the time from the first encounter to the second encounter is 2T hours,
Then: the driving distance from the beginning to the first encounter is 40t, and the driving distance from the first encounter to the second encounter is 40 * 2T
So: the relationship between the distance of a and the total distance is: 40 * 4t-80 = 2S
Similarly, the relationship between the distance of B and the total distance is: (40-8) * 4T + 80 = 2S
It can be concluded that:
T = 5 (hours), s = 360 (kilometers)
That is, the distance between the two stations is 360 km
I'm glad to answer for you. I wish you progress in your study
If you don't understand, you can ask! If you agree with my answer
Please click the "select as satisfactory answer" button below, thank you!

If you want to make an expression, you can also make an equation. The equation should be detailed
1. It takes 9 hours for a to walk from the East Village to the West Village, and 5 kilometers per hour for B. If two people travel from the East and west villages at the same time, they can meet in 4 hours. How many kilometers per hour does a travel?

A runs 1 / 9 of the whole journey per hour, 4 hours 1 / 9 × 4 of the whole journey, and B runs 5 × 4 = 20 (km) in 4 hours, accounting for 1-1 / 9 × 4 of the whole journey
Whole course: 5 × 4 ÷ (1-1 / 9 × 4) = 36 (km)
A 36 × 1 / 9 per hour = 4 (km)