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

b) \(x^3-3x^2+3x-9=x^2\left(x-3\right)+3\left(x-3\right)=\left(x-3\right)\left(x^2+3\right)\)

c) xem lại đề

d) \(9-x^2-2xy-y^2=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)

A = xy + y - 2x - 2

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

= ( x + 1 )( y - 2 )

B = x² - 3x + xy - 3y

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

= ( x - 3 )( x + y )

C = 3x² - 3xy - 5x + 5y

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

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

D = xy + 1 + x + y

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

= ( x + 1 )( y + 1 )

E = ax - bx + ab - x²

= ( ax - x² ) + ( ab - bx )

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

= ( a - x )( x + b )

F = x² + ab + ax + bx

= ( ax + x² ) + ( ab + bx )

= x( a + x ) + b( a + x )

= ( a + x )( x + b )

G = a³ - a²x - ay + xy

= a²( a - x ) - y( a - x )

= ( a - x )( a² - y )

Bonus : = ( a - x )[ a² - ( √y )² ]

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

H = 2xy + 3z + 6y + xz

= ( 6y + 2xy ) + ( 3z + xz )

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

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

A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1

B = x² - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)

C = 3x² - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)

D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)

E = ax - bx + ab - x² = ax - x² + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)

F = x² + ab + ax + bx = ab + ax + bx + x² = a(b + x) + x(b + x) = (a + x)(b + x)

G = a³ - a²x - ay + xy = a²(a - x) - y(a - x) = (a² - y)(a - x)

H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)

🍀Trần Nhật Quỳnh🍀 y không dương nên không thể cho vào căn nhé 

\(a,xy+1-x-y\)

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

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

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

\(b,ax+ay-3x-3y\)

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

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

\(c,x^3-2x^2+2x-4\)

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

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

\(d,x^2+ab+ax+bx\)

\(=\left(x^2+ax\right)+\left(ab+bx\right)\)

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

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

\(e,16-x^2+2xy-y^2\)

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

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

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

\(f,ax^2+ax-bx^2-bx-a+b\)

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

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

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

a)x^2+2x-4y^2-4y

=(x²-4y²)+(2x-4y)

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

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

b)x^4-6x^3+54x-81

=(x⁴-81)+(-6x³+54x)

=(x²-9)(x²+9)-6x.(x²-9)

=(x²-9)(x²+9-6x)

=(x-3)(x+3)(x-3)²

=(x-3)³(x+3)

c)ax^2+ax-bx^2-bx-a+b

=(ax²-bx²)+(ax-bx)+(-a+b)

=x².(a-b)+x.(a-b)-(a-b)

=(a-b)(x²+x+1)

Bài 1 : 

a ) \(x^2-6x-y^2+9=\left(x^2-6x+9\right)-y^2=\left(x-3\right)^2-y^2=\left(x-3+y\right)\left(x-3-y\right)\)

b)  \(25-4x^2-4xy-y^2=5^2-\left(4x^2+4xy+y^2\right)=5^2-\left(2x+y\right)^2=\left(5+2x+y\right)\left(5-2x-y\right)\)

c)  \(x^2+2xy+y^2-xz-yz=\left(x+y\right)^2-z.\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)

d)   \(x^2-4xy+4y^2-z^2+4tz-4t^2=\left(x^2-4xy+4y^2\right)-\left(z^2-4tz+4t^2\right)\)

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

BÀi 2 : 

a)   \(ax^2+cx^2-ay+ay^2-cy+cy^2=\left(ax^2+cx^2\right)-\left(ay+cy\right)+\left(ay^2+cy^2\right)\)

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

b)   \(ax^2+ay^2-bx^2-by^2+b-a=\left(ax^2-bx^2\right)+\left(ay^2-by^2\right)-\left(a-b\right)\)

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

c)  \(ac^2-ad-bc^2+cd+bd-c^3=\left(ac^2-ad\right)+\left(cd+bd\right)-\left(bc^2+c^3\right)\)

\(=-a.\left(d-c^2\right)+d.\left(b+c\right)-c^2.\left(b+c\right)=\left(b+c\right).\left(d-c^2\right)-a\left(d-c^2\right)\)

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

BÀi 3 : 

a)  \(x.\left(x-5\right)-4x+20=0\) \(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x-4\right)=0\)

\(\Leftrightarrow\hept{\begin{cases}x-5=0\\x-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=5\\x=4\end{cases}}}\)

b)  \(x.\left(x+6\right)-7x-42=0\)\(\Leftrightarrow x.\left(x+6\right)-7.\left(x+6\right)=0\) \(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)

\(\Leftrightarrow\hept{\begin{cases}x+6=0\\x-7=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-6\\x=7\end{cases}}}\)

c)   \(x^3-5x^2+x-5=0\) \(\Leftrightarrow x^2.\left(x-5\right)+\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x^2+1\right)\)

\(\Leftrightarrow\hept{\begin{cases}x^2+1=0\\x-5=0\end{cases}\Leftrightarrow\hept{\begin{cases}x^2=-1\left(KTM\right)\\x=5\end{cases}}}\)

d)   \(x^4-2x^3+10x^2-20x=0\) \(\Leftrightarrow x.\left(x^3-2x^2+10x-20\right)=0\)\(\Leftrightarrow x.\left[x^2.\left(x-2\right)+10.\left(x-2\right)\right]=0\)  \(\Leftrightarrow x.\left(x-2\right)\left(x^2+10=0\right)\)

\(\Leftrightarrow\hept{\begin{cases}x=0\\x-2=0\\x^2+10=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=2\\x^2=-10\left(KTM\right)\end{cases}}}\)

a) ko bt làm

ax - ay + bx - by= (ax - ay) + (bx - by)

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

                    = (x - y)(a + b)

x² - 2xy + y² - 1= (x² - 2xy + y²) - 1² 

                             = (x - y)²  - 1² 

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

9 - x² - 2xy - y² = 3² - ( x² + 2xy + y² )

                         = 3² - ( x + y)² 

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

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

a ) xy + 1 - x - y

= x ( y - 1 ) + 1 - y

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

= ( x - 1 ) ( y - 1 )

b ) x² + ab + ac + bx

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

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

= ( b + x ) ( x + a ) ( b + c )

c ) ax + bx - cx + a + b - c

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

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

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