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

=(-2x+y)(4x+y)

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

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

=3(x+1)(3x-5)

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

=-[(x^2+1)^2-(2x)^2]

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

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

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

=3x(x+2)

5: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(2x^2+2)*4x

=8x(x^2+1)

6: =(5x-5y)^2-(4x+4y)^2

=(5x-5y-4x-4y)(5x-5y+4x+4y)

=(x-9y)(9x-y)

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

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

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

8: =(x^2+4y^2-20-4xy+16)(x^2+4y^2-20+4xy-16)

=[(x-2y)^2-4][(x+2y)^2-36]

=(x-2y-2)(x-2y+2)(x+2y-6)(x+2y+6)

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

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

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

d) \(y^2\left(x-1\right)-7y^3+7xy^3\)

\(=y^2\left(x-1-7y+7xy\right)\)

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

a)

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

b)

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

sorry ! mk đang học lớp 6

a) 1/2(x³+8)=1/2(x+2)(x²-2x+4)

b) x⁴(x-y)+2x³(x-y)=x³(x+2)(x-y)

c) x²-(y²-6y+9)=x²-(y-3)²=(x-y+3)(x+y-3)

d) xy(x³+y³)=xy(x+y)(x²-xy+y²)

e)3x²(x²-25y²)=3x²(x-5y)(x+5y)

f) 4x⁴+4x²y²+y⁴-4x²y²= (2x²+y²)²-(2xy)²=(2x²-2xy+y²)(2x²+2xy+y²)

a) \(\frac{1}{2}x^3+4=\frac{1}{2}\left(x^3+8\right)=\frac{1}{2}\left(x+2\right)\left(x^2-2x+4\right)\)

b) \(x^5-x^4y+2x^4-2x^3y=x^3\left(x^2-xy+2x-2y\right)=x^3\left[x\left(x-y\right)+2\left(x-y\right)\right]=x^2\left(x-y\right)\left(x+2\right)\)

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

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

e) \(3x^4-75x^2y^2=3x^2\left(x^2-25y^2\right)=3x^2\left(x+5y\right)\left(x-5y\right)\).

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

a) \(9\left(2x-3\right)^2-4\left(x+1\right)^2\)

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

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

\(=\left(4x-11\right)\left(8x-7\right)\)

b) \(\left(x^2+4y^2-20\right)-16\left(xy-4\right)^2\)

\(=\left[\left(x^2-4xy+4y^2\right)-4\right]\left[\left(x^2+4xy+4y^2\right)-36\right]\)

\(=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]\)

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

a. 9 ( 2x - 3 )² - 4 ( x + 1 )²

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

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

= ( 6x - 9 - 2x - 2 ) ( 6x - 9 + 2x + 2 )

= ( 4x - 11 ) ( 8x - 7 )

b. ( x² + 4y² - 20 )² - 16 ( xy - 4 )²

= ( x² + 4y² - 20 )² - [ 4 ( xy - 4 ) ]²

= [ x² + 4y² - 20 - 4 ( xy - 4 ) ] [ x² + 4y² - 20 + 4 ( xy - 4 ) ]

= ( x² + 4y² - 20 - 4xy + 16 ) ( x² + 4y² - 20 + 4xy - 16 )

 = ( x² + 4y² - 4xy - 4 ) ( x² + 4y² + 4xy - 36 )

= [ ( x - 2y )² - 2² ] [ ( x + 2y )² - 6² ]

= ( x - 2y - 2 ) ( x - 2y + 2 ) ( x + 2y - 6 ) ( x + 2y + 6 )

a) 9( 2x - 3 )² - 4( x + 1 )²

= 3²( 2x - 3 )² - 2²( x + 1 )²

= [ 3( 2x - 3 ) ]² - [ 2( x + 1 ) ]²

= ( 6x - 9 )² - ( 2x + 2 )²

= [ ( 6x - 9 ) - ( 2x + 2 ) ][ ( 6x - 9 ) + ( 2x + 2 ) ]

= ( 6x - 9 - 2x - 2 )( 6x - 9 + 2x + 2 )

= ( 4x - 11 )( 8x - 7 )

b) ( x² + 4y² - 20 )² - 16( xy - 4 )²

= ( x² + 4y² - 20 )² - 4²( xy - 4 )²

= ( x² + 4y² - 20 )² - [ 4( xy - 4 ) ]²

= ( x² + 4y² - 20 )² - ( 4xy - 16 )²

= [ ( x² + 4y² - 20 ) - ( 4xy - 16 ) ][ ( x² + 4y² - 20 ) + ( 4xy - 16 ) ]

= ( x² + 4y² - 20 - 4xy + 16 )( x² + 4y² - 20 + 4xy - 16 )

= [ ( x² - 4xy + 4y² ) - 4 ][ ( x² + 4xy + 4y² ) - 36 ]

= [ ( x - 2y )² - 2² ][ ( x + 2y )² - 6² ]

= ( x - 2y - 2 )( x - 2y + 2 )( x + 2y - 6 )( x + 2y + 6 )