Junior 2 Math Problems: Factoring and Finding Process???

Glad to answer for you :

Solution: x-1-x(x-1)+x(x-1) 2-x(x-1) 3+...x(x-1)^2003+x(x-1)^2004

x-1)[1-x+x(x-1)-x(x-1)^2+..x(x-1)^2002+x(x-1)^2003]

x-1)(1-x)[1-x-x(1-x)(x-1)(1-x)(1-x)[1-x-)-x(1-x)^2000-x(1-x)^2001]

x-1)(1-x)^2004

x-1) 2005 Hope!

7(x+3)(x-3)

a(a-1)

3(a+b)(a-b)

x-y)(a+b+c)

m+n)(x-y+1)

I did a little bit, it's actually quite simple, it's too much, you can refer to it and learn the skills.

Is there a question number, too much dear.

There are so many questions that no one has the leisure to explain them to you.

a²+2b²+c²-2ab-2bc=(a²+b²-2ab)+(b²+c²-2bc)=0

So a=b=c

Therefore, the triangle is equilateral.

2. a²-16b²-c²+6ab+10bc=（a²+9b²+6ab）-(25b²+c²-10bc)=0

So a=-3b c=5b

Hence a+c=2b

So (A2 - 2AB + B 2) +B 2 - 2BC + C 2) = 0

So (a - b) 2 + b-c) 2 = 0 because both square terms are non-negative, but the sum is 0, so both are 0, so a=b, b=c

So it's an equilateral triangle.

So (A2 + 6AB + 9B2) -25B2 - 10BC + C2) = 0

So(a + 3b) 2 - 5b - c) 2 = 0, so (a + 3b+5b -c)(a + 3b - 5b + c) = 0

So (a +8b - c)(a - 2b + c) = 0 because a + b > c, so a+8b - c>0 so a - 2b + c = 0

So a+c = 2b

=(m+n)²-6（m+n）+9

m+n-3）²

The point is to look at M+N as a whole.

Solution: (1) The cube of 3ax - 108ax = 3ax (x 2-36) = 3ax (x-6) (x + 6).

2) 81a to the 4th power -1 = (9a 2-1) (9a 2+1) = (3a-1) (3a + 1) (9a 2 + 1).

3) (5a-b) squared + 20ab = 25a 2-10ab + b 2 + 20ab = 25a 2 + 10ab + b 2 = (5a + b) 2

4) 16x cube - 4x = 4x (4x 2-1) = 4x (2x-1) (2x + 1).

5) 2x squared y-8xy+8y=2y(x 2-4x+4)=2y(x-2) 2

6)3a(x-y)-5b(y-x)=3a(x-y)+5b(x-y)=(3a+5b)(x-y)

[1] 3ax^3-108ax=3ax(x^2-36)=3ax(x-6)(x+6)

2]81a^4-1=(9a^2+1)(9a^2-1)=(9a^2+1)(3a+1)(3a-1)

3](5a-b)^2+20ab=25a^2-10ab+b^2+20b=25a^2+10ab+b^2=(5a+b)^2

4]16x^3-4x=4x(x^2-1)=4x(x+1)(x-1)

5]2(x^2)y-8xy+8y=2y(x^2-4x+4)=2y(x-2)^2

6]3a(x-y)-5b(y-x)=3ax-3ay-5by+5bx=(3a+5b)x-(3a+5b)y

Note: 2 is squared, 3 is cubic, and so on.

1. Original formula = 3ax (x 2-36) = 3ax (x-6) (x + 6)

2. Original formula = (9a 2+1) (9a 2-1) = (9a +1) (3a + 1) (3a-1).

3. Original formula = 25a 2-10ab + b 2 + 20ab = (5a + b) 2

4. Original formula = 2y(x 2-4x+4) = 2y(x-2) 2

5. Original formula = (x-y) (3a+5b).

x+y)^2-4(x+y-1)

x+y)^2-4(x+y)+4

x+y-2)^2

x+y) 2 is the meaning of (x+y) square round. Cover wax skill. Thing key.