a) Ta có: \(a^2-b^2-5a+5b\)

\(=\left(a-b\right)\left(a+b\right)-5\left(a-b\right)\)

\(=\left(a-b\right)\left(a+b-5\right)\)

b) Ta có: \(a^2-b^2-3ab^2-3a^2b\)

\(=\left(a-b\right)\left(a+b\right)-3ab\left(a+b\right)\)

\(=\left(a+b\right)\left(a-b-3ab\right)\)

c) Ta có: \(x^2-xy+2y-4\)

\(=\left(x^2-4\right)-\left(xy-2y\right)\)

\(=\left(x-2\right)\left(x+2\right)-y\left(x-2\right)\)

\(=\left(x-2\right)\left(x+2-y\right)\)

d) Ta có: \(4a^2-10ax+15x-9\)

\(=\left(4a^2-9\right)-\left(10ax-15x\right)\)

\(=\left(2a-3\right)\left(2a+3\right)-5x\left(2a-3\right)\)

\(=\left(2a-3\right)\left(2a+3-5x\right)\)

1. = 2(a+b)

2. =2(a-b)

3.=2(a+2b-3c)

4.=3(a-2b-3c)

5.=-4(a+2b+3c)

6.=-5(x+2xy+3y)

7.=-7(a+2ab+3b)

8.=6(xy-2x-3y)

9.=8(xy-3y+2x)

10.=9(ab-2a+1)

Lần sau bn cần ghi đề rõ ràng hơn

11.=x(y-1)

12.=a(x+1)

13.=m(x+y+1)

14.=-a(x+y+1)

15.=-a(x²+x+1)

16.=-2a(x+2y)

17.=2a(x-y+1)

18.=2(2ax-ay-2)

19.=5a(1-2x-3)

20.=-2ab(a+2b+3)

a) \(6a^2b^2c-4ab^2c^2+12a^2bc^2\)

\(=2abc\left(3ab-2bc+6ac\right)\)

b)\(x^2\left(x-y\right)-y\left(y-x\right)\)

\(=x^2\left(x-y\right)+y\left(x-y\right)\)

\(=\left(x-y\right)\left(x^2+y\right)\)

c) \(6x\left(x-1\right)+9x^2\left(x-1\right)\)

\(=\left(x-1\right)\left(6x+9x^2\right)\)

\(=3x\left(x-1\right)\left(2+3x\right)\)

4a²b² + 36a²b³ + 6ab⁴

= 2ab²(2a + 18ab + 3b²)

3n(m - 3) + 5m(m - 3)

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

2a(x - y) - (y - x)

= (x - y)(2a + 1)

4a²b³ - 6a³b²

= 2a²b²(2b - 3a)

Phân tích đa thức thành nhân tử

a. 3ab ( x+ y) - 6ab ( y+ x)

   =( x + y) ( 3ab - 6ab )

     = ( x +y ) ( - 3ab)

b.7a (x - 3)+a²(x² - 9)

  =7a( x- 3) + a² ( x² - 3²)

  =7a ( x - 3 ) + a² ( x- 3 ) ( x+3 )

   = ( x- 3) . 7a + a² ( x + 3)

    = ( x- 3) ( 7a +a²x + 3a²)

c. 34 (x + y) -x -y

  = 34 ( x+ y) - ( x+y)

 =(x +y ) ( 34 - 1) = 33 ( x+ y)

  d. 25 x⁴  - 94²

     =( 5x² )² - 94²

     =( 5x² - 94 ) ( 5x²+94)

   e.( 5a - b )² - ( 2a +3b)²

      =( 5a -b -2a - 3b) (5a -b + 2a + 3b)

       =(3a - 4b) (7a+ 2b)

 k. 2² -3a - b² +3b

    =( 2² - b² ) + ( -3a +3b)

    =( 2-b) (2+b) + 3( -a +b)

mk làm đầu tiên nhớ tick cho mk nhé!!

\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)

\(a,15a^2b^3+5a^3b^2=5a^2b^2\left(3b+a\right)\\ b,x^2-2x+1-y^2=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\)

a) 15a²b³+5a³b²=5a²b²(3b+a)
b) x²-2x+x-y²=( x²-y²⁾-(2x+x)
                     =(x-y)(x+y)-x(2-1)
                      =(x-y)(x+y)-x3