If f (x + y) = f (x) + F (y) + 2XY [x, y belong to R] f (1) = 2, then f (- 3)=

If f (x + y) = f (x) + F (y) + 2XY [x, y belong to R] f (1) = 2, then f (- 3)=

If f (0 + 0) = f (0) + F (0) + 0, then f (0) = 0
If f (1-1) = f (1) + F (- 1) - 2, f (- 1) = 0
If f (- 1-1) = f (- 1) + F (- 1) + 2, f (- 2) = 2
Then f (- 3) = f (- 1-2) = f (- 1) + F (- 2) + 4 = 6

It is known that the function FX is an odd function defined on R, and for any x1, X2, it always has fx1-fx2 △ x1-x2 > 0,
If a f (3) > F (- 5) B F (- 3) > F (- 5) C f (- 5) > F (3) d f (- 5) < f (- 3), B and D are the same

[f(x1)-f(x2)]/(x1-x2)>0
F (x1) - f (x2) and x1-x2 have the same sign and are not 0
X 1F (x 2), the function increases monotonically over the domain R
So the question a, B, D are tenable, the question should be the wrong one, so the two same answers, the teacher did not specifically correct

For X1 less than X2, if FX1 is less than or equal to FX2, then why is there equal to in the definition of monotone increasing function? Who can explain it?

Some books define simple increasing function in this way
If F X 1 is less than f x 2, it is called strictly monotone function
Different books have different agreements. Pay attention to them when you read them

Factorization by extracting common factor
1.2a²-6a³
2.8ab²-16a³b³
3.-15xy-5x²
4.-xy²+2x²y-xy
5.a³b³+a²b²-ab
6.-3a³m-6a²m+12am
7.（x+2y）²+x+2y
8.15x（a-b）²-3y（b-a）

1.2a²-6a³=2a²（1-3a）2.8ab²-16a³b³= 8ab²（1-2a²b）3.-15xy-5x² =-5x（x+3y）4.-xy²+2x²y-xy =-xy（y-2x+1）5.a³b³+a²b²-ab=ab（a&#...

Ask a few questions about the factorization of the common factor method
1.ax+ay
2.3mx-6my
3.4A M2 + 10ab
4.15x square - 5x
5.15a square + 25ab
6.3x cubic + 6x square
7.4x cubic - 6x square
8. - x squared - XY XZ
9. - x squared y-xy squared
10. - 12abc + 3bC square

1. ax+ay=a(x+y)
2. 3mx-6my=3m(x-2y)
3.4A square + 10ab = 2A (2a + 5b)
4. 15x square - 5x = 5x (3x-1)
5. 15A square + 25ab = 5A (3a + 5b)
6. 3x cube + 6x square = 3x ^ 2 (x + 2)
7. 4x cube-6x square = 2x ^ 2 (2x-3)
8. - x square - xy-xz = - x (x + y + a)
9. - x square, y-xy square = - XY (x + y)
10. - 12abc + 3bC square = 3bC (c-4a)

Several questions about factorization
1、（X-2)^2-2(X-2)=___________
2. If P · q = 0, then P=___ Or q=___
3. If (X-2) (2x + 3) = 0, then X-2=___ Or 2x + 3=___ From which we get X=___ Or X=___

1、（X-2)^2-2(X-2)=(X-2)(X-2-2)=(X-2)(X-4)
2. If P · q = 0, then p = 0 or q = 0
3. If (X-2) (2x + 3) = 0, then X-2 = 0 or 2x + 3 = 0, the solution is x = 2 or x = - 1.5

Several factorization problems
It is known that a, B and C are the three sides of △ ABC, and the square of a + the square of bc-ac-b = 0
The square of 1-x - the square of 2x-y
The square of (x + y) - XY

a^2+b^2+c^2=ab+bc+ac
2(a^2+b^2+c^2)=2(ab+bc+ac)
a^2-2ab+b^2+b^2-2bc+c^2+a^2-2ac+c^2=0
(a-b)^2+(b-c)^2+(a-c)^2=0
If one of them is greater than 0, then at least one of them is less than 0
So all three are zero
(A-C) ^ 2 = 0, i.e. a = C
(B-C) ^ 2 = 0, i.e. B = C
(a-b) ^ 2 = 0, i.e. a = b
a=b=c
ABC is an equilateral triangle

How to factorize these questions
x^2y＋x^2z-xy^2-y^2z
3a^2-2b^2+5ab-2a+3b-1
x^2-y^2+4y-4
ab(a+b)+bc(b+c)+ca(c+a)+2abc

1.x^2y＋x^2z-xy^2-y^2z=(x^2y-xy^2)+(x^2z-y^2z)=xy(x-y)+z(x-y)(x+y)=(x-y)(xy+xz+yz)2.3a^2-2b^2+5ab-2a+3b-1=(a+2b-1)(3a-b+1)3.x^2-y^2+4y-4=x^2-(y^2-4y+4)=x^2-(y-2)^2=(x-y+2)(x+y-2)4.ab(a+b)+bc(b+c)+ca(c...

Some questions about factorization
1. Fill in the blanks: (A-3) (A & sup2; + 2) + (- A + 3) (2a & sup2; - 3) = (A-3) ()
2. 2A & sup2; x-2ax + Half X
3. Factorization first, and then evaluate (x + 1) (2x-3) + 2 (x + 1) (3-2x) + (x + 1) & sup2; (2x-3), where x = half
4. Using the knowledge of factorization, it is shown that 3 to the 24th power - 1 can be divisible by 28
5. Given that a = 2009, B = 2010, C is a rational number, find the value of algebraic formula half (a + C) & sup2; + half (B + C) & sup2; - (a + C) (B + C)

1.a-3)(a²+2)+(-a+3)(2a²-3)=(a-3)(-a^2+5)
2.2a² x-2ax+x/20=x(2a^2-2a+1/20)
3.（x+1）（2x-3)+2(x+1)(3-2x)+(x+1)²(2x-3)=(x+1)(2x-3)(1-2+x+1))
=x(x+1)(2x-3)=1/2(1/2+1)(1-3)=-3/2
4.3 ^ 24-1 = (3 ^ 12 + 1) (3 ^ 12-1) = (3 ^ 12 + 1) (3 ^ 6 + 1) (3 ^ 6-1) = (3 ^ 12 + 1) (3 ^ 6 + 1) (3 ^ 3 + 1) (3 ^ 3-1) = = (3 ^ 12 + 1) (3 ^ 6 + 1) * 28 * 26 can be divided by 28
5.（a+c）²/2+（b+c）²/2-（a+c)(b+c)=1/2[(（a+c）²+（b+c）²-2（a+c)(b+c)]=1/2[(a+c)-(b+c)]^2
=1/2(a-b)^2=1/2*(2009-2010)^2=1/2

Can you help me with the problem of factorization?
(1) a^2-c^2+ab-cb
= (a-c)(a+c+b)
(2)m^2-n^2+2m-2n
=(m-n)(m+n+2)
(3) a^2-b^2-2a+1
=(a-1-b)(a-1+b)
(4)1-m^2-n^2+2mn
=(1-m+n)(1+m-n)
(5)a^2+2ab+b^2-ac-bc
=(a+b)(a=b-c)
(6) a^2+b^2-2ab-10a+10b+25
=(a-b+5)^2
(7)x^4y-x^2y+2x^3 y^2-2xy^2
=xy(x+2y)(x-1)(x+1)
This time, it's more complicated. Can you help me? I have no confidence in myself. I may make a lot of mistakes. Can you check it for me? If it's wrong, please tell me the number of mistakes. And you'd better give me the correct solution to the calculation process, OK?