b) \(5x-5y+ax-ay \)

\(=\left(5x-5y\right)+\left(ax-ay\right)\)

\(=5.\left(x-y\right)+a.\left(x-y\right)\)

\(=\left(x-y\right)\left(5+a\right)\)

c) \(a^3-a^2x-ay+xy\)

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

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

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

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

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

3 ) \(5x-5y+ax-ay=5.\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(5+a\right)\)

4 ) \(a^3-a^2x-ay+xy=a^2.\left(a-x\right)-y.\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)

5 ) \(xy.\left(x+y\right)+yz.\left(y+z\right)+xz.\left(x+z\right)+2xyz\)

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

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

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

\(=\left(x+y\right)\left(xy+yz+z^2+xz\right)=\left(x+y\right)\left[\left(xy+xz\right)+\left(yz+z^2\right)\right]\)

\(=\left(x+y\right)\left[x.\left(y+z\right)+z.\left(y+z\right)\right]=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

a) \(x^2-x-y^2+y\)

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

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

b) \(x^2-2xy-z^2+y^2\)

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

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

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

c) \(5x-5y+ax-ay\)

\(=5\left(x-y\right)+a\left(x-y\right)\)

\(=\left(x-y\right)\left(5+a\right)\)

a) x² - x - y² - y

= (x^2 - y^2) - (x+y)

= (x+y) (x-y) - (x+y)

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

b) x² - 2xy - z² + y²

= (x^2 - 2xy + y^2 ) - z^2 

= (x-y)^ 2- z^2

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

c) 5x - 5y + ax - ay

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

= (5+a)(x-y)

a) x² - x - y² - y  =  (x² - y²) - (x+y) = (x-y)(x+y) - (x+y) = (x+y). ( x- y - 1)

b) x² - 2xy - z² + y²  = (x² - 2xy + y² ) - z² = (x-y)² - z² = (x-y+z) . (x-y-z)

c) 5x - 5y + ax - ay = 5.(x-y) + a(x-y) = (5+a) . ( x-y) 

\(5x-5y+ax-ay\)

\(=5\left(x-y\right)+a\left(x-y\right)\)

\(=\left(x-y\right)\left(5+a\right)\)

\(5x-5y+ax-ay\)

\(=\left(5x-5y\right)+\left(ax-ay\right)\)

\(=5\left(x-y\right)+a\left(x-y\right)\)

\(=\left(x-y\right)\left(5+a\right)\)

5x-5y+ax-ay

<=>5(x-y)+a(x-y)

<=>(x-y)(5+a)

1) x² - x - y² - y = (x - y)(x + y) - (x + y) = (x - y - 1)(x + y)

2. x² - 2xy + y² - z² = (x - y)² - z² = (x - y - z)(x - y + z)

3. 5x - 5y + ax - ay = 5(x - y) + a(x - y) = (a + 5)(x - y)

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

5. 4x² - y² + 4x + 1 = (2x + 1)² - y² = (2x + 1 - y)(2x  + y + 1)

6. x³ - x + y³ - y = (x + y)(x² - xy + y²) - (x + y) = (x + y)(x² - xy + y² - 1)

Trả lời:

1, x² - x - y² - y

= ( x² - y² ) - ( x + y )

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

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

2, x² - 2xy + y² - z²

= ( x² - 2xy + y² ) - z²

= ( x - y )² - x²

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

3, 5x - 5y + ax - ay

= ( 5x + ax ) - ( 5y + ay )

= x ( 5 + a ) - y ( 5 + a )

= ( 5 + a ) ( x - y )

= ( 5 + a ) ( x - y )

4, a³ - a²x - ay + xy

= ( a³ - a²x ) - ( ay - xy )

= a² ( a - x ) - y ( a - x )

= ( a - x ) ( a² - y )

5, 4x² - y² + 4x + 1

= ( 4x² + 4x + 1 ) - y² 

= ( 2x + 1 )² - y²

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

6, x³ - x + y³ - y

= ( x³ + y³ ) - ( x + y )

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

= ( x + y ) ( x² - xy + y - 1 )

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) 

5x-5y+ax-ay = 5(x-y) +a(x-y) = (x-y)(5+a)

b) a^3 -a^2x-ay+xy = a^2(a-x) -y(a-x) = (a-x)(a^2-y)

c) xy(x+y) +yz(y+z) +xz(x+z) +2xyz = x^2.y+xy^2 +y^2.z+xz^2 +x^2.z+xz^2 +2xyz

= (x^2.y+x^2.z)+(xy^2+xz^2+2xyz)+(y^2.z+yz^2) = x^2(y+z) +x.(y+z)^2 +yz(y+z)

=(y+z)(x^2+x+yz)

\(x^2-2xy+y^2-z^2\)

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

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

\(x^2-2xy+y^2-z^2\)

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

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

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

(x²-2xy+y²⁾-z²

<=>(x-y)²-z²

<=>(x-y-z)(x-y+z)

\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\)

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

\(10x^2+10xy+5x+5y=10x\left(x+y\right)+5\left(x+y\right)=5\left(2x+1\right)\left(x+y\right)\) \(5ay-3bx+ax-15by=a\left(5y+x\right)-3b\left(5y+x\right)=\left(a-3b\right)\left(5y+x\right)\) \(x^3+x^2-x-1=x^2\left(x+1\right)-\left(x+1\right)=\left(x^2-1\right)\left(x+1\right)=\left(x+1\right)^2\left(x-1\right)\) \(2bx-3ay-6by+ax=x\left(2b+a\right)-3y\left(2b+a\right)=\left(x-3y\right)\left(2b+a\right)\)

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