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 )

a,x^2-x-y^2-y

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

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

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

b, x^2-2xy+y^2-z^2

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

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

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

c,5x-5y+ax-ay( đề bài ở đây phải là -ay ms tính đc)

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

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

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

d,a^3-a^2.x-ay+xy

=(a^3-a^2x)-(ay-xy)

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

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

e,4x^2-y^2+4x+1

={(2x)^2+4x+1}-y^2

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

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

f,x^3-x+y^3-y

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

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

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

a: =5(2x+3y)

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

a: =(x^2-x+1)(x^2+x+1)

b: =x^2-6xy+9y^2=(x-3y)^2

c: =5x(x^2-2xy+y^2)

=5x(x-y)^2

d: =(x-3)^2

e: =(2y-z)(4x+7y)

a)HĐT:(x^2+1-x)(x^2+1+x)

b)=x^2-2.x.3y+(3y)^2

c)=5x(x^2-2xy+y^2)

=5x(x-y)^2

d)x^2-2.3.x+3^2

=(x-3)^2

e)(2y-z)+7y(2y-z)

=(2y-z)(1+7y)

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

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

2)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)

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

\(ax+bx+ay+by\)

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

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

\(xy+1-x-y\)

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

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

\(x^2-y^2-5x-5y\)

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

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

a) \(x^2-x-y^2-y\)

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

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

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

b) \(x^2-2xy+y^2-z^2\)

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

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

c) \(5x-5y+ax-ay\)

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

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