Urgency to solve math problems with factorization

3（x+3y）（x+y）+y²

0+4y²=4y².There's something wrong with the title.

2a-b）²+6a+3b）-4

2a-b+1）（2a-b-4）.

3.The sum of the product of any four consecutive positive integers and 1 is the square of a positive integer. Here's why:

Let four consecutive positive integers be a, a+1, a+2, a+3, then a(a+1)(a+2)(a+3)+1

a（a+3）】【a+1）（a+2）】+1（a²+3a）（a²+3a+2）+1

a²+3a）²+2（a²+3a）+1

a²+3a+1）².

Therefore, the sum of the product of any four consecutive positive integers and 1 is the square of a positive integer.

1.Solve the system of equations, x=, y=, and substitute the solution.

2.Observe the equation, substitution factor, so that c=2a

Substituting c in, then there is c -2cb+b -3c+3b-4, why is it treated like this, because it is easier to deal with the coefficient of the quadratic term into one, and when the coefficient of the quadratic term becomes 1, use the pending coefficient method.

Let the decomposition be: (c-b+n)(c-b+m).

After that, c -2cb+b +(m+n)c-(m+n)b+mn and the formula c -2cb+b -3c+3b-4 have the corresponding coefficients are, m+n=-3, mn=-4

obtained, m=-4, n=1

Therefore, the factorization is: (c-b+1)(c-b-4) substituting c=2a into (2a-b+1)(2a-b-4)3Again, this is a factorization problem.

First, assuming that the four consecutive positive integers are n, n+1, n+2, n+3 factorized decomposition subs, n(n+1)(n+2)(n+3)+1 first, n 4+6n 3+11n 2+6n+1 observe the given example, and guess that the number on the right may be equal to the square of (n+1)(n+2)-1.

The guessed formula, n 4 + 6n 3 + 11n 2 + 6n + 1, is found to be true.

So there is n(n+1)(n+2)(n+3)+1=((n+1)(n+2)-1) 2

So you can shout out loud that the sum of the product of any four consecutive positive integers and 1 is the square of a positive integer.

(7 to the power of 16 + 1) (7 to the power of 16 - 1).

7 to the power of 16 + 1) (7 to the power of 4 + 1) (7 to the power of 4 - 1) == (7 to the power of 16 + 1) (7 to the power of 4 + 1) (7 + 1) (7 to the power of 16) (7 to the power of 16 + 1) (7 to the power of 4 + 1) 50 4850 and 48

1.Variable sign, -3b(z-y) = 3b(y-z), original formula = 2a(y-z) + 3b(y-z), extract common factor (y-z), original formula = (2a+3b)(y-z).

2.Extract the common factor (p+q), the original formula = (6p-4q) (p+q).

3.Variable sign, 2(3-a)=-2(a-3), original formula = m(a-3)-2(a-3), extract common factor (a-3), original formula = (m-2)(a-3).

1. The numerator and denominator are divided by m and n2 to obtain: m (m + n) + m (m-n) -n 2 (m 2-n 2) = 1 (1+n m) + 1 (1-n m)-1 (m2 n2-1).

Bringing in m n = 5 3 gives us 41 16

2. x+1 x=2 both ends are squared at the same time x2+2+1 x2=4 x2+1 x2=2

3. It is obtained: [a(x-2)+b(x-1)] [(x-1)(x-2)]=3x-4 [(x-1)(x-2)].

a(x-2)+b(x-1)=3x-4

a+b)x-(2a+b)=3x-4

a+b=3, and 2a+b=4

Solution; a=1,b=2

①3x^4y^2-12x^3yz

3x³y(xy-4z)

4xy^3+8xy^2-16xy

4xy(y²-2y+4)

4（m-n）^3+8(n-m)^2

4(m-n)³+8(m-n)²

4(m-n)²(m-n+2)

a(2a-b)-2b(b-2a)

a(2a-b)+2b(2a-b)

2a-b)(a+2b)

x^2-9y^2

x-3y)(x+3y)

3ab^3-3ab

3ab(b²-1)

3ab(b-1)(b+1)

5m-2n)^2-9(m+n)^2

5m-2n-3m-3n)(5m-2n+3m+3n)=(2m-5n)(8m+n)⑧=(

9a^2+6a+1

3a+1)²

Question 10 x 3y-6x 2y 2+9xy 3=xy(x -6xy+9y).

xy(x-3y)²

Question 11. a^2+4b^2)^2-16a^2b^2=(a²+4b²-4ab)(a²+4b²+4ab)=(a-2b)²(a+2b)²

Question 12. x^2+4x-y^2-6y-5

x²+4x+4-y²-6y-9

x+2)²-y+3)²

x+2+y+3)(x+2-y-3)

x+y+5)(x-y-1)

The title of Question 10 is incorrect.

①3x^4y^2-12x^3yz

Solution: 3x y (xy-4z).

4xy^3+8xy^2-16xy

Solution: -4xy (y -2y+4).

Others are added.

2.Original (a-b)(3a-3b-6)=3(a-b)(a-b-2)4Original (x-y) 2(x-y)=(x-y) 36

Original 6(a-b) 2(3a-3b-2b)=6(a-b) 2(3a-5b).

8.Original (x+y)(xx-xy-xx-xy)=(x+y)(-2xy)=-2xy(x+y)

There's nothing difficult about this, the last formula extracts an x+y and merges with the previous one.

You can use Xuebajun to take photos and search questions!

4(x+y+z) 2-9(x-y-z) 2 with the squared difference formula =[2(x+y+z)] 2-[3(x-y-z)] 2=[2(x+y+z)+3(x-y-z)][2(x+y+z)-3(x-y-z)].

5x-y-z)(5y+5z-x)

9(x+y) 2+12(x+y)+4 with the perfect square formula =[3(x+y)] 2+2*2*3(x+y)+2 2=[3(x+y)+2] 2

x 2+9) 2-36x 2 use the square difference formula = [x 2+9+6x][x 2+9-6x] and then use the perfect square formula.

x+3)^2(x-3)^2

x-y)(x-y-12)+36

x-y) 2-12(x-y)+36 with the perfect square formula =(x-y-6) 2

18m^2-m^4-81

(m 4-18m 2+81) perfect square formula = -(m 2-9) 2 then use the square difference formula = -(m + 3) 2 (m-3) 2

1. =4[(x+y)^2+2(x+y)z+z^2]-9x^2-9y^2-9z^2+18xy+18xz-18yz=-5(x^2+y^2+z^2)+26xy+26xz-10yz

2.=9(x 2+2xy+y 2)+12(x+y)+4 or = 2 2 for squared.

3. =[(x^2+9)-6x][x^2+9+6x]=[(x-3)^2][(x+3)^2]=(x-3)^2 *(x+3)^2

4. =(x-y)^2-12(x-y)+36=[(x-y)-6]^2

5.=18m2-m 4-81=-[(m2) 2-2*9m-9 2]=(m2-9) 2 or =(m squared minus 9) squared.