\(x^4-x^2+2x-1\)

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

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

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

hk

tốt

a) 16x² - ( x² + 4 )²

= ( 4x )² - ( x² + 4 )²

= [ 4x - ( x² + 4 ) ][ 4x + ( x² + 4 ) ]

= ( -x² + 4x - 4 )( x² + 4x + 4 )

= [ -( x² - 4x + 4 ) ]( x + 2 )²

= [ -( x - 2 )² ]( x + 2 )²

b) ( x + y )³ + ( x - y )³

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

= ( x + y + x - y )[ x² + 2xy + y² - ( x² - y² ) + x² - 2xy + y² ]

= 2x( 2x² + 2y² - x² + y²

= 2x( x² + 3y² )

Bài 1:

\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)

Bài 3:

\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)

Bài 1;

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

2) \(6x^2+12xy+6y^2=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\)

3) \(2y^3+8y^3+8y=10y^3+8y=2y\left(5y^2+4\right)\)

4) \(5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)

Bài 2:

1) \(x^3-64x=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\)

2) \(8x^2y-18y=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\)

3) \(24x^3-3=3\left(8x^3-1\right)=3\left(2x-1\right)\left(4x^2+2x+1\right)\)

Bài 3:

1) \(5x^2+10x+5-5y^2=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y\right]=5\left(x-y+1\right)\left(x+y+1\right)\)

2) \(3x^3-6x^2+3x-12xy^2=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=3x\left(x-2y-1\right)\left(x+2y-1\right)\)

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

4) \(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2-4x+4y\right)=2x\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]=2x\left(x-y\right)\left(x+y-4\right)\)

( a + b )³ - ( a³ + b³ )

= a³ + 3a²b + 3ab² + b³ - a³ - b³

= 3a²b - 3ab²

= 3ab ( a + b )

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

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

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

\(=3ab\left(a+b\right)\)

Phân tích các đa thức sau thành nhân tử:

(a+b)^3-(a^3+b^3) = 3a . b . (b+a)

nha bạn chúc bạn học tốt nha 

:)))))))))

cái này có những biểu thức ko dùng được hđt hoặc đặt nhân tử chung =))) anh nghĩ đề em nên thay chữ và thành hoặc 

1, \(15x^2+10xy=5x\left(3x+2y\right)\)

2, \(24x-18y+30=6\left(4x-3y+5\right)\)

3, \(2x\left(y-2009\right)+5y\left(y-2009\right)=\left(y-2009\right)\left(2x+5y\right)\)

4, \(35x\left(y-8\right)-14y\left(8-y\right)=\left(y-8\right)\left(35x+14y\right)=7\left(5x+2y\right)\left(y-8\right)\)

5, \(x^2+14x+49=x^2+2.7x+7^2=\left(x+7\right)^2\)

6, \(9x^2-4=\left(3x-2\right)\left(3x+2\right)\)

Trả lời:

1, 15x² + 10xy = 5x ( 3x + 2y )

2, 24x - 18y + 30 = 6 ( 4x - 3y + 5 )

3, 2x ( y - 2009 ) + 5y ( y - 2009 ) = ( y - 2009 )( 2x + 5y )

4, 35x ( y - 8 ) - 14y ( 8 - y ) = 35x ( y - 8 ) + 14y ( y - 8 ) = ( y - 8 )( 35x + 14y ) = 7 ( y - 8 )( 5x + 2y )

5, x² + 14x + 49 = ( x + 7 )² 

6, 9x² - 4 = ( 3x - 2 )( 3x + 2 )

a, \(\left(4x+5\right)^2=\left(4x+5\right)\left(4x+5\right)=\left[\left(4x+5\right)4x\right]+\left[\left(4x+5\right)5\right]=4x^2+20x+25\)

b, \(\left(5x-2\right)^2=\left(5x-2\right)\left(5x-2\right)=\left[\left(5x-2\right)5x-\left(5x-2\right)2\right]=5x^2-10x+25\)

b, \(8^2-12x^2=\left(8^2-12x^2\right)\left(8^2+12x^2\right)\)

đúng ko :) 

@No name: Bị sai rồi nhé, a,b,c sai hết  :>

a) ( 4x + 5 )² 

= ( 4x )² + 2.4x.5 + 5² 

= 16x² + 40x + 25 

b) ( 5x - 2 )² 

= ( 5x )² - 2.5x.2 + 2² 

= 25x² - 20x + 4 

c) 8² - 12x² 

= 64 - 12x² 

= ( V8 - V12x )( V8 + V12x ) 

*V    là căn 

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

= 2x(4x + 2)

Em áp dụng hđt số 3 trong sgk nhé.

(3x+1+x+1) (3x+1-x-1) = (4x+2) 2x

                                      = 4x(2x+1)

sorry ! mk đang học lớp 6

Ta có:  x⁶ -y⁶= (x³)²  -(y³)²  = (x³  - y³)(x³ + y³)

\(x^6-y^6\)

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

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

hk 

tốt

\(\left(x-2\right)^3-1=\left(x-2\right)\left[\left(x-3\right)^2+x-2\right]=\left(x-2\right)\left(x^2+5x+7\right)\)

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

\(\left(x+3\right)^2-\left(x-1\right)^2=4\left(2x+4\right)=8\left(x+2\right)\)

a) \(\left(x-2\right)^3-1=\left(x-2\right)^3-1^3=\left(x-2-1\right)\left[\left(x-2\right)^2+\left(x-2\right)\cdot1+1^2\right]\)\(=\left(x-3\right)\left(x^2-4x+4+x-2+1\right)\)

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

b) \(\left(x+3y\right)^2-9y^2\)

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

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

\(=x\left(x+6y\right)\)

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

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

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

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