If the fifth power of polynomial x + (2m-1) the third power of x-7x + 5n-2 does not contain cubic term and constant term, find the value of 4 times the square of M-15 times the square of n

If the fifth power of polynomial x + (2m-1) the third power of x-7x + 5n-2 does not contain cubic term and constant term, find the value of 4 times the square of M-15 times the square of n

There is no cubic term and constant term
be
2m-1=0
5n-2=0
The solution is m = 1 / 2, n = 2 / 5
So 4m & sup2; - 15N & sup2; = - 7 / 5
Find junior two factorization questions and their answers 100, clear point
x^(x-y)+(y-x)=(x-y)(x^-1)=(x-y)(x-1)(x+1)
25x^2-16y^2
=(5x+4x)(5x-4x)
When what is the value of X, the sum of 43x-5 and 3x + 1 is equal to 9?
From the meaning of the question: 43x-5 + 3x + 1 = 9, to the denominator: 4x-15 + 9x + 3 = 27, to shift and merge: 13X = 39, coefficient into 1: x = 3
Factorization, 1 / 2ab-1 / 2B square - (a-b) square
1 / 2ab-1 / 2B square - (a-b) square
=1/2b(a-b)-(a-b)²
=(a-b)(1/2b-a+b)
=(a-b)(3/2b-a)
Speed to 100 factorization and answer. Speed (good) chasing points!
When what is the value of X, the sum of 43x-5 and 3x + 1 is equal to 9?
From the meaning of the question: 43x-5 + 3x + 1 = 9, to the denominator: 4x-15 + 9x + 3 = 27, to shift and merge: 13X = 39, coefficient into 1: x = 3
Factorization: the square of 16 (a-2b) - (a + b)
Use the square difference formula to solve the problem
Square of 16 (a-2b) - (a + b)
=(4a-8b-a-b)(4a-8b+a+b)
=(3a-9b)(5a-7b)
16(a-2b)²-(a+b)²=16（a²-4ab+4b²）-(a²+2ab+b²)
=15a²-66ab+63b²=3(5a²-22ab+21b²)=3(5a-7b)(a-3b)
100 factoring questions and answers
fast
1. Factorize the following
（1）12a3b2－9a2b+3ab;
（2）a（x+y）－（a－b）（x+y）;
（3）121x2－144y2;
（4）4（a－b）2－（x－y）2;
（5）（x－2）2+10（x－2）+25;
（6）a3（x+y）2－4a3c2.
2. Simple calculation
（1）6.42－3.62;
（2）21042－1042
（3）1.42×9－2.32×36
The second chapter decomposes the factor synthesis exercise
1、 Multiple choice questions
1. The deformation from left to right in the following formulas is factorized as ()
(A)(a+3)(a-3)=a2-9 (B)x2+x-5=(x-2)(x+3)+1
(C)a2b+ab2=ab(a+b) (D)x2+1=x(x+ )
2. The correct one in the factorization of the following formulas is ()
(A)-a2+ab-ac= -a(a+b-c) (B)9xyz-6x2y2=3xyz(3-2xy)
(C)3a2x-6bx+3x=3x(a2-2b) (D) xy2+ x2y= xy(x+y)
3. Factorize the polynomial M2 (A-2) + m (2-A) into ()
(A)(a-2)(m2+m) (B)(a-2)(m2-m) (C)m(a-2)(m-1) (D)m(a-2)(m+1)
4. The following polynomials can decompose factors ()
(A)x2-y (B)x2+1 (C)x2+y+y2 (D)x2-4x+4
5. In the following polynomials, the one that can't be decomposed by the complete square formula is ()
(A) (B) (C) (D)
6. If the polynomial 4x2 + 1 is added with a monomial to make it the complete square of an integer, then the added monomial cannot be ()
(A)4x (B)-4x (C)4x4 (D)-4x4
7. The following factorization is wrong ()
(A)15a2+5a=5a(3a+1) (B)-x2-y2= -(x2-y2)= -(x+y)(x-y)
(C)k(x+y)+x+y=(k+1)(x+y) (D)a3-2a2+a=a(a-1)2
8. In the following polynomials ()
(A)-a2+b2 (B)-x2-y2 (C)49x2y2-z2 (D)16m4-25n2p2
9. The following Polynomials: ① 16x5-x; ② (x-1) 2-4 (x-1) + 4; ③ (x + 1) 4-4x (x + 1) + 4x2; ④ - 4x2-1 + 4x
(A)①② (B)②④ (C)③④ (D)②③
10. The square difference of two consecutive odd numbers can always be divided by K, then K is equal to ()
(A) Multiple of 4 (b) 8 (c) 4 or - 4 (d) 8
2、 Fill in the blanks
11. Decomposition factor: m3-4m =
12. Given x + y = 6, xy = 4, then the value of X2Y + XY2 is
13. If the factorization result of XN yn is (x2 + Y2) (x + y) (X-Y), then the value of n is
14. If AX2 + 24x + B = (MX-3) 2, then a =, B =, M =. (photo 15)
15. Observe the figure. According to the relationship between the area of the figure, you can get a formula to decompose the factor without connecting other lines. This formula is
3、 (6 points for each question, 24 points in total)
16. Factorization: (1) - 4x3 + 16x2-26x (2) A2 (x-2a) 2-A (2a-x) 3
（3）56x3yz+14x2y2z－21xy2z2 (4)mn(m－n)－m(n－m)
17. Factorization: (1) 4xy – (x2-4y2) (2) - (2a-b) 2 + 4 (a-b) 2
18. Factorization: (1) - 3ma3 + 6ma2-12ma (2) A2 (X-Y) + B2 (Y-X)
19. Factorization
（1） ； （2） ；
（3） ；
20. Factorization: (1) ax2y2 + 2axy + 2A (2) (x2-6x) 2 + 18 (x2-6x) + 81 (3) - 2x2n-4xn
21. Factorize the following formulas:
（1） ； （2） ； （3） ；
22. Factorization (1); (2);
23. A simple calculation method is used
(1)57.6×1.6+28.8×36.8-14.4×80 (2)39×37-13×34
（3）．13.7
The square difference of two consecutive odd numbers is twice the sum of the two consecutive odd numbers
25. As shown in the figure, in the four corners of a square cardboard with side length of a cm, cut out a square with side length of B (b <) cm, and calculate the remaining area by factorization when a = 13.2 and B = 3.4
26. Factorize the following
（1）
（2） ；
(3) (4)
(5)
(6)
(7) (8)
(9) （10）(x2+y2)2-4x2y2
（12）．x6n+2+2x3n+2+x2 （13）．9(a+1)2(a-1)2-6(a2-1)(b2-1)+(b+1)2(b-1)2
27. Given (4x-2y-1) 2 + = 0, find the value of 4x2y-4x2y2 + XY2
28. Known: a = 10000, B = 9999, find the value of A2 + b2-2ab-6a + 6B + 9
29. Prove that 58-1 solution is divisible by two integers between 20 and 30
30. Write a polynomial, and then decompose it into factors (requirements: the polynomial contains letters M and N, with unlimited coefficients and times, and can be decomposed by extracting common factors first and then formula method)
31. Observe the following formula:
12+(1×2)2+22=9=32
22+(2×3)2+32=49=72
32+(3×4)2+42=169=132
……
What rule do you find? Please use the equation containing n (n is a positive integer) and explain the reason
32. Read the following factorization process and then answer the questions raised:
1+x+x(x+1)+x(x+1)2=(1+x)[1+x+x(x+1)]
=(1+x)2(1+x)
=(1+x)3
(1) The above factorization method is applied times
(2) If we decompose 1 + X + X (x + 1) + X (x + 1) 2 + +X (x + 1) 2004
(3) Decomposition factor: 1 + X + X (x + 1) + X (x + 1) 2 + +X (x + 1) n (n is a positive integer)
34. If a, B and C are the three sides of △ ABC, and satisfy A2 + B2 + C2 AB BC CA = 0. Explore the shape of △ ABC and explain the reason
35. Read the following calculation:
99×99+199=992+2×99+1=（99+1）2=100 2=10 4
1. Calculation:
999×999+1999=____________ =_______________ =_____________ =_____________ ;
9999×9999+19999=__________ =_______________ =______________ =_______________ .
2. Guess 99999999999 × 999999999 + 199999999999 is equal to? Write the calculation process
36. There are several small balls of the same size, one by one, just placed in an equilateral triangle (as shown in Figure 1); put these balls in another way, one by one, just placed in a square (as shown in Figure 2). How many such balls are there at least?
Figure 1 Figure 2
When what is the value of X, the sum of 43x-5 and 3x + 1 is equal to 9?
From the meaning of the question: 43x-5 + 3x + 1 = 9, to the denominator: 4x-15 + 9x + 3 = 27, to shift and merge: 13X = 39, coefficient into 1: x = 3
Square of a + square of B + 2ab-2a-2b + 1 = factorization
The original formula = (a + b) & # - 2 (a + b) + 1
=(a+b-1)²