It is known that the set a is equal to {a, B plus a, a plus 2B}, and B is equal to {the square of C in a, AC, AC}. If a is equal to B, find the value of C

It is known that the set a is equal to {a, B plus a, a plus 2B}, and B is equal to {the square of C in a, AC, AC}. If a is equal to B, find the value of C

A must be equal to a,
If a + B = a C, a + 2 b = a C,
The solution is b = 0, C = 1,
A is equal to {a, a, a}, which does not satisfy the mutual dissimilarity of elements in the set
If a + 2 b = a C, a + B = a C,
The solution is b = - (3 A) / 4, C = - 1 / 2,
Another set of solutions B = 0, C = 1, rounding off
Factorization exercises and answers
You really want so many questions
1. 5ax+5bx+3ay+3by
Solution: = 5x (a + b) + 3Y (a + b)
=(5x+3y)(a+b)
2. x^3-x^2+x-1
Solution: = (x ^ 3-x ^ 2) + (x-1)
=x^2(x-1)+ (x-1)
=(x-1)(x^2+1)
3. x2-x-y2-y
Solution: = (x2-y2) - (x + y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y-1)
bc(b+c)+ca(c-a)-ab(a+b)
=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=(bc+ca)(c-a)+(bc-ab)(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)．
x^2+3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5)．
(x ^ 2 + X + 1) (x ^ 2 + X + 2) - 12, y = x ^ 2 + X, then
Original formula = (y + 1) (y + 2) - 12
=y^2+3y+2-12=y^2+3y-10
=(y+5)(y-2)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)．
(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
Original formula = (1 + y) ^ 2 + 2 (1 + y) x ^ 2 (1 + y) + x ^ 4 (1-y) ^ 2-2 (1 + y) x ^ 2 (1-y) - 2x ^ 2 (1 + y ^ 2)
=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)
=[(1+y)+x^2(1-y)]^2-(2x)^2
=[(1+y)+x^2(1-y)+2x]·[(1+y)+x^2(1-y)-2x]
=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)
=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]
=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)
x^5+3x^4y-5x^3y^2+4xy^4+12y^5
Original formula = (x ^ 5 + 3x ^ 4Y) - (5x ^ 3Y ^ 2 + 15x ^ 2Y ^ 3) + (4xy ^ 4 + 12Y ^ 5)
=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)
=(x+3y)(x^4-5x^2y^2+4y^4)
=(x+3y)(x^2-4y^2)(x^2-y^2)
=(x+3y)(x+y)(x-y)(x+2y)(x-2y)
Decomposition factor M + 5n-mn-5m
m +5n-mn-5m= m -5m -mn+5n
= (m -5m )+(-mn+5n)
=m(m-5)-n(m-5)
=(m-5)(m-n)
Decomposition factor BC (B + C) + Ca (C-A) - AB (a + b)
bc(b+c)+ca(c-a)-ab(a+b)=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)
1.(2a-b)²+8ab
2.y²-2y-x²+1
3.x²-xy+yz-xz
4.6x²+5x-4
5.2a²-7ab+6b²
6.(x²-2x)²+2(x²-2x)+1
7.(x²-2x)²-14(x²-2x)-15
8.x²(x-y)+(y-x)
9.169(a+b)²-121(a-b)²
10.(x-3)(x-5)+1
Answer: 1. (2a-b) & sup2; + 8ab = (2a + b) & sup2;
2.y²-2y-x²+1=(y-1)²-x²=(y-1-x)(y-1+x)
3.x²-xy+yz-xz =x(x-y)-z(x-y)=(x-z)(x-y)
4.6x²+5x-4 =(2x-1)(3x+4)
5.2a²-7ab+6b²=(2a-3b)(a-2b)
6.(x²-2x)²+2(x²-2x)+1 =(x²-2x+1)²=(x-1)^4
7.(x²-2x)²-14(x²-2x)-15 =(x²-2x-15)(x²-2x+1)=(x+3)(x-5)(x-1)²
8.x²(x-y)+(y-x) =(x²-1)(x-y)=(x+1)(x-1)(x-y)
9.169(a+b)²-121(a-b)²
=(14a+14b-11a+11b)(14a+14b+11a-11b)
=(3a+25b)(25a+3b)
10.(x-3)(x-5)+1 =(x-3)²-2(x-3)+1 =(x-3-1)²=(x-4)²
-5a^2+16a=a(16-5a)
8x^2-4x=4x(2x-1)
15p+10p^2＝5p(3+2p)
－3x^2y-6xy=-3xy(x+2y)
14m^3n^2-6m^2n^3=2m^2n^2(7m-6n)
27a^2 b^3 c+18ab^2=9ab^2(3abc+2)
18xy^2 z^3+12x^2 y^2=6xy^2(3z^3+2x)
8m^2 n^2 -6m^3 n^2=2m^2 n^2(4-3m)
Factorization 3a3b2c-6a2b2c2 + 9ab2c3 = 3AB ^ 2 C (a ^ 2-2ac + 3C ^ 2)
3. Factorization XY + 6-2x-3y = (x-3) (Y-2)
4. Factorization X2 (X-Y) + Y2 (Y-X) = (x + y) (X-Y) ^ 2
5. Factorization 2x2 - (a-2b) x-ab = (2x-a) (x + b)
6. Factorization a4-9a2b2 = a ^ 2 (a + 3b) (a-3b)
7. If it is known that X3 + 3x2-4 contains a factor of X-1, try to decompose X3 + 3x2-4 = (x-1) (x + 2) ^ 2
8. Factorization AB (x2-y2) + XY (A2-B2) = (ay + BX) (AX by)
9. Factorization (x + y) (a-b-c) + (X-Y) (B + C-A) = 2Y (a-b-c)
10. Factorization a2-a-b2-b = (a + b) (a-b-1)
11. Factorization (3a-b) 2-4 (3a-b) (a + 3b) + 4 (a + 3b) 2 = [3a-b-2 (a + 3b)] ^ 2 = (a-7b) ^ 2
12. Factorization (a + 3) 2-6 (a + 3) = (a + 3) (A-3)
13. Factorization (x + 1) 2 (x + 2) - (x + 1) (x + 2) 2 = (x + 1) (x + 2) ABC + ab-4a = a (BC + B-4)
(2)16x2－81＝(4x+9)(4x-9)
(3)9x2－30x＋25＝(3x-5)^2
(4)x2－7x－30＝(x-10)(x+3)
35. Factorization x2-25 = (x + 5) (X-5)
36. Factorization x2-20x + 100 = (X-10) ^ 2
37. Factorization x2 + 4x + 3 = (x + 1) (x + 3)
38. Factorization 4x2-12x + 5 = (2x-1) (2x-5)
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40. Factorization (x + 2) (x-3) + (x + 2) (x + 4) = (x + 2) (2x-1)
41. Factorization 2ax2-3x + 2ax-3 = (x + 1) (2ax-3)
42. Factorization 9x2-66x + 121 = (3x-11) ^ 2
43. Factorization 8-2x2 = 2 (2 + x) (2-x)
44. Factorization x2-x + 14 = integer cannot be decomposed
45. Factorization 9x2-30x + 25 = (3x-5) ^ 2
46. Factorization - 20x2 + 9x + 20 = (- 4x + 5) (5x + 4)
47. Factorization 12x2-29x + 15 = (4x-3) (3x-5)
48. Factorization 36x2 + 39x + 9 = 3 (3x + 1) (4x + 3)
49. Factorization 21x2-31x-22 = (21x + 11) (X-2)
50. Factorization 9x4-35x2-4 = (9x ^ 2 + 1) (x + 2) (X-2)
51. Factorization (2x + 1) (x + 1) + (2x + 1) (x-3) = 2 (x-1) (2x + 1)
52. Factorization 2ax2-3x + 2ax-3 = (x + 1) (2ax-3)
53. Factorization x (y + 2) - x-y-1 = (x-1) (y + 1)
54. Factorization (x2-3x) + (x-3) 2 = (x-3) (2x-3)
55. Factorization 9x2-66x + 121 = (3x-11) ^ 2
56. Factorization 8-2x2 = 2 (2-x) (2 + x)
57. Factorization x4-1 = (x-1) (x + 1) (x ^ 2 + 1)
58. Factorization x2 + 4x-xy-2y + 4 = (x + 2) (X-Y + 2)
59. Factorization 4x2-12x + 5 = (2x-1) (2x-5)
60. Factorization 21x2-31x-22 = (21x + 11) (X-2)
61. Factorization 4x2 + 4xy + y2-4x-2y-3 = (2x + Y-3) (2x + y + 1)
62. Factorization 9x5-35x3-4x = x (9x ^ 2 + 1) (x + 2) (X-2)
Given X-Y + 3, find the value of 3x & # 178; - 6xy + 3Y & # 178
The building lord, your head portrait is a poem, jade, is also a little poem
3x²-6xy+3y²
=3(x²-2xy+y²)
=3(x-y)²
=3×3²
=27
x-y=3
3x²-6xy+3y²
=3(x²-2xy+y²)
=3(x-y)²
=3×3²
=27
How to do the square of (3a-2b + C) (two methods)
Original formula = 3A (3a-2b + C) - 2b (3a-2b + C) + C (3a-2b + C)
=9a²-6ab+3ac-6ab+4b²-2bc+3ac-2bc+c8
Merge yourself
The original formula = [(3a-2b) + C] ²
=(3a-2b)²+2(3a-2b)c+c²
=9a²-12ab+4b²+6ac-4bc+c²
Factorization exercises in grade one of junior high school
The original formula = 3x ~ - 3xy-x ~ - x = 3x (X-Y) - x (x + 1) = x (3x-3y-x-1) = x (2x-3y-1) 3
1．m2(p－q)－p＋q；
2．a(ab＋bc＋ac)－abc；
3．x4－2y4－2x3y＋xy3；
4．abc(a2＋b2＋c2)－a3bc＋2ab2c2；
5．a2(b－c)＋b2(c－a)＋c2(a－b)；
6．(x2－2x)2＋2x(x－2)＋1；
7．(x－y)2＋12(y－x)z＋36z2；
8．x2－4ax＋8ab－4b2；
9．(ax＋by)2＋(ay－bx)2＋2(ax＋by)(ay－bx)；
10．(1－a2)(1－b2)－(a2－1)2(b2－1)2；
11．(x＋1)2－9(x－1)2；
12．4a2b2－(a2＋b2－c2)2；
13．ab2－ac2＋4ac－4a；
14．x3n＋y3n；
15．(x＋y)3＋125；
16．(3m－2n)3＋(3m＋2n)3；
17．x6(x2－y2)＋y6(y2－x2)；
18．8(x＋y)3＋1；
19．(a＋b＋c)3－a3－b3－c3；
20．x2＋4xy＋3y2；
21．x2＋18x－144；
22．x4＋2x2－8；
=x(2x-3y-1) 3
What are you asking, and where did the last three come from
Let 2x & # 178; + 3x-6 be expressed as a (x-1) &# 178; + B (x + 1) + C
First of all, we can determine a = 2, expand the first part, the coefficient of the first term is - 4, which is required to be + 3, so B = 7, and finally the constant term. The constant terms obtained from the first two terms are 2 and 7 respectively, which together is 9, which is required to be - 6, so C = - 15
How to calculate the square of the sum of three digits, for example: (a + 2B + C) square, and (a + 2b-c), (a-2b + C)
Factoring test questions in grade one of junior high school
①32a（x^2+x）^2+2a
②16+8（x^2+4x）+（x^2+4x）^2
③3x^(n)y+9x^(n-1)y^2+1/4x^(n+1)
① There is something wrong with the title, which should be - 2A, otherwise it can't be decomposed into 32A [(x ^ 2 + 2x) ^ 2] - 2A = 2A [16 (x ^ 2 + 2x) ^ 2-1] = 2A (4x ^ 2 + 8x + 1) (4x ^ 2 + 8x-1) ② 16 + 8 (x ^ 2 + 4x) + (x ^ 2 + 4x) ^ 2 = (4 + x ^ 2 + 4x) ^ 2 = (x ^ 2 + 4x + 4) ^ 2 = (x + 2) ^ 4 ③ 3x ^ NY + 9x ^ (n-1) y ^ 2 + x ^ (n + 1) / 4
1/2-x=1/x-2-6-x/3x²-12
That number can't be used. It can't be kicked
Multiply both sides by 3 (X-2) (x + 2)
-3(x+2)=3(x+2)-(6-x)
-3x-6=3x+6-6+x
7x=-6
x=-6/7
Test: x = - 6 / 7 is the solution of the equation
The solution of the equation is x = - 6 / 7
The original formula can be converted to
-1/2-x=1/(x-2)-(6-x/3(x²-4))
(2/x-2)-(6-x/3(x-2)(x+2))=0
Simplify
(7x+6)/3(x-2)(x+2)=0
7x+6=0
∴x=-6/7
(a + b) (a-b) - 5 (the square of a-2b) factorization factor