A = 10ax - 5ay - 2x + y

= ( 10ax - 5ay ) - ( 2x - y )

= 5a( 2x - y ) - ( 2x - y )

= ( 2x - y )( 5a - 1 )

B = 2x² - 6xy + 5x - 15y 

= 2x( x - 3y ) + 5( x - 3y )

= ( x - 3y )( 2x + 5 )

C = ax² - 3axy + bx - 3by

= ( ax² + bx ) - ( 3axy + 3by )

= x( ax + b ) - 3y( ax + b )

= ( ax + b )( x - 3y )

D = 2ax³ + 6ax² + 6ax + 18a

= 2ax²( x + 3 ) + 6a( x + 3 )

= ( x + 3 )( 2ax² + 6a )

= ( x + 3 )2a( x² + 3 )

E = 5x²y + 5xy² + a²x + a²y ( đã sửa 1 dấu '-' )

= 5xy( x + y ) + a²( x + y )

= ( x + y )( 5xy + a² )

F = 10xy² - 5by² + 2a²x - aby ( xem lại đề chứ không phân tích được :)) )

\(2ax-bx+3cx-2a+b-3c\\ =x\left(2a-b+3c\right)-\left(2a-b+3c\right)\\ =\left(x-1\right)\left(2a-b+3c\right)\)

\(ax-bx-2cx-2a+2b+4c\\ =x\left(a-b-2c\right)-2\left(a-b-2c\right)\\ =\left(x-2\right)\left(a-b-2c\right)\)

\(3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\)

\(ax^2-bx^2-2ax+2bx-3a+3b\\ =x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a+b\right)\\ =\left(x^2-2x-3\right)\left(a+b\right)\\ =\left(x+1\right)\left(x-3\right)\left(a+b\right)\)

\(1,2x^2-6xy+5x-15y\)

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

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

\(2,ax^{2\:}-3axy+bx-3by\)

\(=ax\left(x-3y\right)+b\left(x-3y\right)\)

\(=\left(x-3y\right)\left(ax+b\right)\)

\(3,5ax^2-3axy+3ay^2-3axy\) ( Đề sai )

Sửa : \(3ax^2-3axy+3ay^2-3axy\)

\(=3ax\left(x-y\right)+3ay\left(y-x\right)\)

\(=3ax\left(x-y\right)-3ay\left(x-y\right)\)

\(=3a\left(x-y\right)^2\)

\(4,4acx+4bcx+4ax+4bx\)

\(=4cx\left(a+b\right)+4x\left(a+b\right)\)

\(=4x\left(a+b\right)\left(c+1\right)\)

\(6,ax^{2\:}y-bx^2y-ax+bx+2a-2b\)

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

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

\(7,ax^{2\:}-bx^2-2ax+2bx-3a+3b\)

\(=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2-2x-3\right)\)

\(8,ax^{2\:}-5x^2-ax+5x+a-5\)

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

\(=\left(a-5\right)\left(x^2-x+1\right)\)

\(9,ax+bx+cx-2a-2b+2c\) Đề sai

Sửa :\(ax+bx+cx-2a-2b-2c\)

\(=x\left(a+b+c\right)-2\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(x-2\right)\)

\(10,2ax-bx+3cx-2a+b-3c\)

\(=\left(2ax-2a\right)-\left(bx-b\right)+\left(3cx-3c\right)\)

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

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

Mấy câu đề sai mk sửa chỗ nào ko đúng thì nói mk nha !

A = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )

= 4x( ac + bc + a + b )

= 4x[ c( a + b ) + ( a + b ) ]

= 4x( a + b )( c + 1 )

B = ax - bx + cx - 3a + 3b - 3c

= x( a - b + c ) - 3( a - b + c )

= ( a - b + c )( x - 3 )

C = 2ax - bx + 3cx - 2a + b - 3c

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

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

D = ax - bx - 2cx - 2a + 2b + 4c

= x( a - b - 2c ) - 2( a - b - 2c )

= ( a - b - 2c )( x - 2 )

E = 3ax² + 3bx² + ax + bx + 5a + 5b

= 3x²( a + b ) + x( a + b ) + 5( a + b )

= ( a + b )( 3x² + x + 5 )

F = ax² - bx² - 2ax + 2bx - 3a + 3b

= x²( a - b ) - 2x( a - b ) - 3( a - b )

= ( a - b )( x² - 2x - 3 )

= ( a - b )( x² + x - 3x - 3 )

= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]

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

Bài 2:

a) x(x - 3)- y(3 - x)

= x(x - 3) + y(x - 3)

= (x - 3)(x + y) (1)

Thay x = \(\frac{1}{3}\); y = \(\frac{8}{3}\)vào (1)

Ta có: (\(\frac{1}{3}\)- 3)(\(\frac{1}{3}\)+ \(\frac{8}{3}\))

= \(\frac{-8}{3}\). 3

= -8

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

a) Ta có: \(4\left(2-x\right)^2+xy-2y\)

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

\(=\left(x-2\right)\left[4\left(x-2\right)+y\right]\)

\(=\left(x-2\right)\left(4x-8+y\right)\)

b) Ta có: \(3a^2x-3a^2y+abx-aby\)

\(=3a^2\left(x-y\right)+ab\left(x-y\right)\)

\(=\left(x-y\right)\left(3a^2+ab\right)\)

\(=a\left(x-y\right)\left(3a+b\right)\)

c) Ta có: \(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)

\(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)\)

\(=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]\)

\(=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-yx+y^2-y^2\right]\)

\(=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)\)

d) Ta có: \(2ax^3+6ax^2+6ax+18a\)

\(=2ax^2\left(x+3\right)+6a\left(x+3\right)\)

\(=\left(x+3\right)\left(2ax^3+6a\right)\)

\(=2a\left(x+3\right)\left(x^3+3\right)\)

e) Ta có: \(x^2y-xy^2-3x+3y\)

\(=xy\left(x-y\right)-3\left(x-y\right)\)

\(=\left(x-y\right)\left(xy-3\right)\)