a) x³ - 1 + 5x² - 5 + 3x - 3

= x³ + 5x² + 3x - 9

= x³ + 6x² - x² + 9x - 6x - 9

= ( x³ + 6x² + 9x ) - ( x² + 6x + 9 )

= x( x² + 6x + 9 ) - ( x² + 6x + 9 ) 

= ( x² + 6x + 9 )( x - 1 )

= ( x + 3 )²( x - 1 )

b) a⁵ + a⁴ + a³ + a² + a + 1

= ( a⁵ + a⁴ + a³ ) + ( a² + a + 1 )

= a³( a² + a + 1 ) + 1( a² + a + 1 )

= ( a² + a + 1 )( a³ + 1 )

= ( a² + a + 1 )( a + 1 )( a² - a + 1 )

c) x³ - 3x² + 3x - 1 - y³

= ( x³ - 3x² + 3x - 1 ) - y³

= ( x - 1 )³ - y³

= ( x - 1 - y )[ ( x - 1 )² + ( x - 1 )y + y² ]

= ( x - 1 - y )( x² - 2x + 1 + xy - y + y² ) 

d) 5x³ - 3x²y - 45xy² + 27y³

= ( 5x³ - 45xy² ) - ( 3x²y - 27y³ )

= 5x( x² - 9y² ) - 3y( x² - 9y² )

= ( 5x - 3y )( x² - 9y² )

= ( 5x - 3y )[ x² - ( 3y )² ]

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

** Sửa: $125x^3-5x-3y+27y^3$
-------------

Lời giải:

$125x^3-5x-3y+27y^3=(125x^3+27y^3)-(5x+3y)$

$=[(5x)^3+(3y)^3]-(5x+3y)$

$=(5x+3y)(25x^2-15xy+9y^2)-(5x+3y)$

$=(5x+3y)(25x^2-15xy+9y^2-1)$

\(5x^3-3x^2y-45xy^2+27y^3\)

\(=x^2\left(5x-3y\right)-9y^2\left(5x-3y^{ }\right)\)

\(=\left(5x-3y\right)\left(x^2-9y^2\right)\)

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

Nhân dịp đầu năm chúc bạn luôn học giỏi , chăm ngoan , ....

\(5x^3-3x^2y-45xy^2+27y^3\\ =\left(5x^3-3x^2y\right)-\left(45xy^2-27y^3\right)\\ =x^2\left(5x-3y\right)-9y^2\left(5x-3y\right)\\ =\left(x^2-9y^2\right)\left(5x-3y\right)\\ =\left(x+3y\right)\left(x-3y\right)\left(5x-3y\right)\)

5x³-3x²y -45xy² +27y³

=x²(5x-3y) -9y²(5x-3y)

=(5x-3y)(x²-9y²)

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

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

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

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

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

3: \(=2\left(x+2\right)\left(25x-15-x\right)\)

\(=2\left(x+2\right)\left(24x-15\right)\)

=6(x+2)(8x-5)

a: \(12x^3-6x^2+3x\)

\(=3x\cdot4x^2-3x\cdot2x+3x\cdot1\)

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

b: \(\dfrac{2}{5}x^2+5x^3+x^2y\)

\(=x^2\cdot\dfrac{2}{5}+x^2\cdot5x+x^2\cdot y\)

\(=x^2\left(\dfrac{2}{5}+5x+y\right)\)

c: \(14x^2y-21xy^2+28x^2y^2\)

\(=7xy\cdot2x-7xy\cdot3y+7xy\cdot4xy\)

\(=7xy\left(2x-3y+4xy\right)\)

a) 5x³y - 30x²y + 45xy

= 5xy.(x² - 6x + 9)

= 5xy.(x² - 2.3.x + 3²)

= 5xy.(x-3)²

b) x³ - 2x² - x+2

= x².(x-2) - (x-2)

= (x-2).(x²-1)

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

c) 3x.(x-y) - (y-x)²

= 3x.(x-y) - (x-y)²

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

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

a) xy+3x-7y-21

=x(y+3)-7(x+3)

=(x-7)(y+3)

b)2xy-15-6x-5y

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

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

c)2x^2y+2xy^2-2x-2y

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

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

x(x+3)-5x(x-5)-5(x+3)

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

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

Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn

a) xy+3x-7y-21=(xy+3x)-(7y+21)= x(y+3)-7(y+3)=(y+3)(x-7)

b)2xy-15-6x+5y=(2xy-6x)+(5y-15)=2x(y-3)+5(y-3)=(y-3)(2x+5)

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

d) x(x+3)-5x(x-5)-5(x+3)=[x(x+3)-5(x+3)]-5x(x-5)=(x+3)(x-5)-5x(x-5)=(x-5)(x+3-5x)=(x-5)(3-4x)