It is known that x2 + 7xy + my2-5x + 43y-24 can be decomposed into two first-order factors of X and Y. try to determine the value of M and complete the factorization

It is known that x2 + 7xy + my2-5x + 43y-24 can be decomposed into two first-order factors of X and Y. try to determine the value of M and complete the factorization

Let x2 + 7xy + my2-5x + 43y-24 = (x + 9y + a) (x-2y + b), after expansion and combination, we get: x2 + 7xy + my2-5x + 43y-24 = x2 + 7xy-18y2 + (a + b) x + (- 2A + 9b) y + AB, ｜ M = − 18a + B = − 5 − 2A + 9b = 43ab = − 24, the solution is: M = − 18a = − 8b = 3, ｜ M = - 18, the original formula = (x + 9y-8) (x-2y + 3)
(x-3) (x-1) (x + 1) (x-3)?
Please give a detailed description of this problem and indicate the calculation method and result. It's better to have a few more similar problems,
（x-3）²（x²-1）
Square difference formula (a + b) (a-b) = A & sup2; - B & sup2;
I'm a teacher. Thank you
The third grade mathematics problem solving equation. To process
1.16X²-24X+9=0
2.3X(X-1)=2-2X
3.X(X+1)=72
1. Factorization
We can get: (4x-3) &# 178; = 0 X1 = x2 = 3 / 4
2. Factorization
We can get: (3x + 2) (x-1) = 0 X1 = - 2 / 3 x2 = 1
3. Factorization
We can get: (x + 9) (X-8) = 0, X1 = - 9, X2 = 8
It's not even tempting to offer a reward
X minus 1 and 3 / 4 x equals 1 / 4
x-7/4x=1/4
-3/4x=1/4
x=-3
It's not easy to play 3x 1 / 4 and substitute it with 7 / 4x
X times (13-x) divided by 2 = 20
x×（13-x）÷2=20
x×（13-x）=40
x^2-13x+40=0
（x-5）（x-8）=0
X1=5 X2=8
The original formula is x * (13-x) = 40
x^2-13x+40=0
(x-5)*(x-8)=0
The solution is X1 = 5
x2=8
The original formula is changed to x times (13-x) = 40 to get x ^ 2-3x + 40 = 0. Finally, (X-5) (X-8) = 0 can be obtained by cross multiplication, and the solutions are x = 5 and x = 8
X ^ 2-13x + 40 = 0 leads to x = 5 or 8
When x = the value of formula 4x + 3 is equal to that of formula 3x + 4
4x + 3 = 3x + 4
4x - 3x = 4 - 3
x = 1
1. In response to the call of "returning farmland to forest" of the state, in a certain place, 1600 hectares of farmland was returned to forest in 2000, and 1936 hectares of farmland was planned to be returned to forest in 2004. What is the average annual growth rate of returning farmland to forest in these two years?
The main thing is every process
Suppose the average annual growth rate of returning farmland to forest is X
1600(1+x)^2=1936
(1+x)^2=1.21
(1+x)= +1.1 or -1.1
X1 = 0.1 = 10% x2 = - 2.1 (rounding)
A: the average annual growth rate of returning farmland to forest is 10%
Let the growth rate be X
1600*[1+X]^2=1936
X=0.1
That is, the growth rate is 10%
It is known that 3x minus 4x is equal to 6, and Y is equal to 6 in the formula of X
3x-4y=6
4y=3x-6
y=(3x-6)/4
3y-4x=6
3y=6+4x
y=(4x+6)/3
With the continuous improvement of people's living standards, the number of family cars in our city has increased year by year. According to statistics, a community has 64 family cars at the end of 2006, and the number of family cars has reached 100 at the end of 2008. (1) if the average annual growth rate of family cars in the community from the end of 2006 to the end of 2009 is the same, how many family cars will the community have by the end of 2009? (2) In order to alleviate the parking contradiction, the community decided to invest 150000 yuan to build several more parking spaces. According to the calculation, the construction costs are 5000 yuan / indoor parking space and 1000 yuan / outdoor parking space respectively. Considering the actual factors, the number of planned outdoor parking spaces is not less than 2 times of that of indoor parking space, but not more than 2.5 times of that of indoor parking space? Try to write out all possible solutions
(1) Suppose that the average annual growth rate of family car ownership is x, then 64 (1 + x) 2 = 100, the solution is X1 = 14 = 25%, X2 = − 94 (out of the question), 100 (1 + 25%) = 125. Answer: by the end of 2009, there will be 125 family cars in the community. (2) a indoor parking space and B outdoor parking space can be built in the community
（3x+___） ²=____ +12xy+____ It is known that: (x-3y) &# 178; = x & # 178; - 6xy + (KY) &# 178;, then K=____ .
（3x+_ 2y__） ²=_ 9x²__ +12xy+_ 4y_ ²__ .
(x-3y) &# 178; = x & # 178; - 6xy + (KY) &# 178;, then k = 3
（3x+2y）²=9x²+12xy+4y²。
(x-3y) &# 178; = x & # 178; - 6xy + (KY) &# 178;, then k = 9