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1.（x+2)^2-(x+y)^3 2.(x-y)^2-(x-y)^3 3.(x-y)^2-(y-x)^3
1, take the common factor (x + y) ^ 2
We get (x + y) ^ 2 (1-x-y) = - (x + Y-1) (x + y) ^ 2
2. Take the common factor (X-Y) ^ 2
We get (X-Y) ^ 2 (1-x + y) = - (x-y-1) (X-Y) ^ 2
(X-Y) ^ 2 + (X-Y) ^ 3 = (X-Y) ^ 2 (1 + X-Y) = (X-Y + 1) (X-Y) ^ 2
The main thing to do is to change the sign when choosing the common factor. When the odd square changes the direction in the brackets, it needs to change the direction of the whole factor, but it doesn't need to change the even square. It's better to simplify the factor according to the positive x direction
9.13 the difficulty of extracting common factor (2)
If you answer more questions well, 100 points will be added
Fill in the blanks:
4. The common factor of - MX (M-X) (x-n) + Mn (M-X) (N-X) is
The common factor of 5.5m (X-Y) & sup2; - 10m & sup2; (Y-X) & sup2; is
The common factor of 6.12a ^ 3 (m-n) ^ 3 + 10A & sup2; (n-m) ^ 3 is
7.a(x-4)(y+3)+b(4-x)(3+y)=(x-4)(y+3)(_____ )
8. Factorize x (x + y) (X-Y) - x (x + y) & sup2; to get
9. (x + y) ^ 3-y (x + y) square + X & sup2; (y + x) = ()_____ )(2x+y)
10.-35x(x+y)-42(x+y)=(_____ )(x+y)(______ )
11. Factorize the following formulas:
1.2x(a²+b²）-3y(a²+b²）
2.（a-b)²-（a-b)(a-c)+(a-b)(b+c)
3.m(a-b)(x+y)-n(b-a)(y+x)
4.x(x-y-z)+y(z-x+y)-z(y-x+z)
5.8(2x+y)^3-12(2x+y)²
6.xy(x-y)²-yz(y-x)²+xz(x-y)²
7.35ab(x-y)²-25a²b²（y-x)²+10ab^3（y-x)^3
8.a(x-y)^2n-a²（y-x)^2n+1+a^3(x-y)^2n
9.3x²（a+3)-4x²y(a+3)
4.m(m-x)(x-n)
5.5m(x-y)²
6.2a²(n-m)^3
7.a-b
8.2x²(x+y)
9.x²+xy
10.- ,35x+42
1. Merge similar items
（2x-3y）(a²+b²)
2. The common factor is A-B, merging
（a-b）(a-b-a+c+b-c)=0
3. The common factor is (a-b) (x + y)
(a-b)(x+y)（m+n）
4. The common factor is y + z-x
-The square of X (y + z-x) + y (y + z-x) + Z (y + z-x) = (y + z-x) (y + z-x) = (y + z-x)
5. The common factor is 4 (2x + y) & sup2;
4(2x+y)²（2（2x+y）+3）=
4(2x+y)²(4x+2y+3)
6. The common factor is (X-Y) & sup2;, merging
(x-y)²（xy-yz+xz）
7. The common factor is 5ab (X-Y) & sup2;
5ab(x-y)²（7-5ab+2b²(y-x)）
8. The common factor is a (X-Y) ^ 2n
A (X-Y) ^ 2n (the square of 1-A + a)
9. The common factor is X & sup2; (a + 3)
x²（a+3)（3-4y）
1999 = [() - ()] times 1999 = () times 1999 - () times 1999 = (.)
1999 of 2000 = [(2 of 2000) - (1 of 2000)] times 1999 = (1 of 1000) times 1999 - (1 of 2000) times 1999 = (0.9995)
168 is the sum of the two prime numbers, and the one digit number of one of them is 1? 168 = () + ()
89 and 79
Is f (x) = x ^ 5 + 2x ^ 3 an odd function
f(-x)=(-x)^5+2(-x)^3
=-(x^5+x^3)
=-f(x)
So f (x) is an odd function
Find the law
1.1 three, 150%, 1,4 three, 60%, () decimal, () fraction, () percentage
90%, 1110%, 0.7, () fraction, () percentage, () decimal
3. () percentage, 0.65115%, () decimal, () fraction, () percentage
Write the rules
1. Three out of one, 150%, 1,4 out of three, 60%, (0.5) decimal, (3 out of seven) fraction, (37.5) percentage rule: the numerator remains unchanged, the denominator is in the order of + 12.90%, 1,5 out of 4110%, 0.7, (6 out of five) fraction, (60% percentage, (1.3) minor rule: odd item 0.1 decreases, even
Eight natural numbers are arranged in a row. Starting from the third number, each number is the sum of the two numbers in front of it. Given that the fifth number is 7, then the eighth number is 7______ ．
Suppose the first number is x, the second number is y, then the third number is x + y, the fourth number is x + 2Y, and the fifth number is 2x + 3Y, that is, 2x + 3Y = 7; because X and y are natural numbers, so x = 2, y = 1; the eighth number is 8x + 13y = 8 × 2 + 13 = 29, so the answer is 29
Let a be the common solution of the equations x ^ 2 - (2k + 1) x + 4 = 0 and 3x ^ 2 - (6k-1) x + 8 = 0, then a =?, k =?
x^2-（2k+1）x+4=0.(1)
3x^2-(6k-1)x+8=0.(2)
(2) - (1) * 3 yes
4x-4=0
x=1
The equation is
1-2k-1+4=0
k=2
So a = x = 1, k = 2
There is a pair of Becks, four, four, more than one, five, five, more than two, six, six, more than three. How many in all?
Four, four, more than one, more than one is equivalent to less than three,
Five, five, more than two, more than two is equivalent to less than three,
Six, six, three more, three less
So there are at least three less than the least common multiple of 4, 5 and 6, that is
4. The least common multiple of 5 and 6 is 60
60-3 = 57
The two even numbers adjacent to the even number 2A (a is a non-zero natural number) are () and ()
The two even numbers adjacent to the even number 2A (a is a non-zero natural number) are (2a-2) and (2a + 2)
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