Bài 1: 

a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)

\(=\left(2x+1\right)\left(3-2x+5\right)\)

\(=\left(2x+1\right)\left(8-2x\right)\)

\(=2\left(4-x\right)\left(2x+1\right)\)

b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)

\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)

\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)

\(=\left(3x-2\right)\left(3x-6\right)\)

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

Bài 2: 

a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

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

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

\(=\left(a-b\right)\left(2a-4b\right)\)

\(=2\left(a-b\right)\left(a-2b\right)\)

f: Ta có: \(x^2-6xy+9y^2+4x-12y\)

\(=\left(x-3y\right)^2+4\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x-3y+4\right)\)

whatterfice

a,\(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

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

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

\(=\left(a-b\right)\left(2a-2b\right)\)

\(=\left(a-b\right)2\left(a-b\right)\)

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

b,\(\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)-\left(y-2x\right)\)

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

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

\(=\left(2x-y\right)\left(4x+1\right)\)

c,\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

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

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

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

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

\(=\left(x-y\right)\left(xy-zx-zy+z^2\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

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

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

= ( a - b )[ ( a + 2b ) + ( 2a - b ) - ( a + 3b ) ]

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

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

= 2( a - b )( a - b ) = 2( a - b )²

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

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

= ( 2x - y )[ ( x + y ) + ( 3x - y ) + 1 ]

= ( 2x - y )( x + y + 3x - y + 1 )

= ( 2x - y )( 4x + 1 )

c) x²( y - z ) + y²( z - x ) + z²( x - y )

= x²y - x²z + y²z - y²x + z²( x - y )

= ( x²y - y²x ) - ( x²z - y²z ) + z²( x - y )

= xy( x - y ) - z( x² - y² ) + z²( x - y )

= xy( x - y ) - z( x - y )( x + y ) + z²( x - y )

= ( x - y )[ xy - z( x + y ) + z² ]

= ( x - y )( xy - zx - zy + z² )

= ( x - y )[ ( xy - zx ) - ( zy - z² ) ]

= ( x - y )[ x( y - z ) - z( y - z ) ]

= ( x - y )( y - z )( x - z )

chuyển về dạng nguyên thể rồi tính thể chất khối lượng sau đó quay về đang tìm mũ của nhiều số làm ra rồi thì dễ lắm bạn ạ k minh nha

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

b)\(\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)

c)\(-2\left(x-4\right)\left(2x+1\right)\)

d)\(\left(x-5\right)\left(4x+1\right)\)

e)\(3\left(x-2\right)\left(3x-2\right)\)

g)\(2\left(a-b\right)^2\)

h)\(\left(xy-3\right)\left(5y^2-2z\right)\)

i)\(\left(4x+1\right)\left(2x-y\right)\)

l)\(abc^2\left(b-a\right)\left(b+c\right)\)

m)\(\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

x² - x - y² - y

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

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

***

9x² + y² - 16z² + 6xy

= (3x + y)² - (4z)²

= (3x + y - 4z)(3x + y + 4z)

***

a³ - a²x - ay + xy

= a²(a - x) - y(a - x)

= (a - x)(a² - y)

***

2x² - 8y² + 3x + 6y

= 2(x² - 4y²) + 3(x + 2y)

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

= (x + 2y)(2x - 4y + 3)

***

xy(x + y) + yz(y + z) + xz(x + z) + 2xyz

= xy(x + y + z) + yz(x + y + z) + xz(x + z)

= y(x + y + z)(x + z) + xz(x + z)

= (x + z)(xy + y² + yz + xz)

= (x + z)[y(x + y) + z(x + y)]

= (x + z)(x + y)(y + z) 

a) \(x^3y^3+125=\left(xy\right)^3+5^3=\left(xy+5\right)\left(x^2y^2-5xy+25\right)\)

b) \(8x^3+y^3-6xy\left(2x+y\right)=\left(8x^3+y^3\right)-6xy\left(2x+y\right)=[\left(2x\right)^3+y^3]-6xy\left(2x+y\right)\)

\(=\left(2x+y\right)\left(4x^2-2xy+y^2\right)-6xy\left(2x+y\right)=\left(2x+y\right)\left(4x^2-2xy+y^2-6xy\right)\)

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

c) \(\left(3x+2\right)^2-2\left(x-1\right)\left(3x+2\right)+\left(x-1\right)^2\)

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

1/Tự chép lại đb nha :v

 =a² - 9b²+2ab+3a²-8b²-12ab+6ab-3b²-2a²+ab

= 2a²-3ab-20b²

= (2a²+5ab) - (8ab+20b²)

= a(2a+5b) - 4b(2a+5b)

=(2a+5b)(a-4b)

câu 2 tương tự nhé :)

a) \(\left(x-3\right)\left(x-1\right)-3\left(x-3\right)\)

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

\(=\left(x-3\right)\left(x-4\right)\)

c) x^2y+xy+x+1=xy(x+1)+x+1=(x+1)(xy+1)    d)x^2-ax-bx+ab=x(x-a)-b(x-a)=(x-a)(x-b)        d)  (x^2-4y^2)-(2x+4y)=(x+2y)(x-2y)-2(x+2y)=(x+2y)(x-2y-2)

a)\((x-3)(x-1)-3(x-3)\)

\(=\left(x-3\right)\left(x-4\right)\)

b)\(x^3-2x^2+2x-13\)

Sai đề

c)\(x^2y+xy+x+1\)

\(=\left(x+1\right)\left(xy+1\right)\)

d)\(x^2-(a+b)x+ab\)

\(=\left(x-a\right)\left(x-b\right)\)

e)\(x^2-2x-4y^2-4y\)

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

Bài làm:

a) \(x^2-2xy+y^2-zx+yz\)

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

\(\left(x-y\right)\left(x-y-z\right)\)

a/ \(x^2-2xy+y^2-zx+yz.\)

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

\(=\left(x-y\right)\left(x-y-z\right)\)

c/ \(x^2-y^2-2x-2y.\)

\(=x^2-2x+1-y^2-2y-1\)

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

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

\(=\left(x-1+y+1\right)\left(x-1-y-1\right)\)

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

sử dụng hằng thành thạo = ez 

\(a,x^2-2xy+y^2-zx+yz\)

\(=\left(x-y\right)\left(x-y\right)-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)

\(b,a^3-3a+3b-b^3=\left(a^3-b^3\right)-3\left(a-b\right)\)

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

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

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

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

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

mấy ý kia không sửa được nữa nên nghỉ:)