f) = x²( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )

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

h) = x³( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 )

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

j) = ( x - y )( x² + xy + y² ) - 3( x - y ) = ( x - y )( x² + xy + y² - 3 )

Trả lời:

f, x³ - 4x² - 9x + 36 = ( x³ - 4x² ) - ( 9x - 36 ) = x² ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x² - 9 ) = ( x - 4 )( x - 3 )( x + 3 )

g, 4x - 4y + x² - 2xy + y² = ( 4x - 4y ) + ( x² - 2xy + y² ) = 4 ( x - y ) + ( x - y )² = ( x - y ) ( 4 + x - y )

h, x⁴ + x³ + x² - 1 = ( x⁴ + x³ ) + ( x² - 1 ) =  x³ ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 ) 

i, x² - y² - 4x - 4y = ( x² - y² ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )

j, x³ - y³ - 3x + 3y = ( x³ - y³ ) - ( 3x - 3y ) = ( x - y )( x² + xy + y² ) - 3 ( x - y ) = ( x - y )( x² + xy + y² - 3 ) 

f) x³-4x²-9x+36

=x²(x-4)-9(x-4)

=(x-4)(x²-9)

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

g) 4x-4y+x²-2xy+y²

=4(x-y)+(x-y)²

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

h) x⁴+x³+x²-1

=x³(x+1)+(x-1)(x+1)

=(x+1)(x³+x-1)

i) x²-y²-4x-4y

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

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

j) x³-y³-3x+3y

=(x-y)(x²+xy+y²)-3(x-y)

=(x-y)(x²+xy+y²-3)

#H

1/   \(4x^2-12xy+9y^2=\left(2x\right)^2-2.2.3xy+\left(3y\right)^2\)

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

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

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

Làm tạm 2 phần đợi mik xíu

4x² - 12xy + 9y² = ( 2x )² - 2.2x.3y + ( 3y )² = ( 2x - 3y )²

x³ - y⁶ = x³  - ( y² )³ = ( x - y² )( x² + xy² + y⁴ )

x⁶ - 6x⁴ + 12x² - 8 = ( x² )³ - 3.(x²)².2 + 3.x².2² - 2³ = ( x² - 2 )³

( x² + 4y² - 5 )² - 16( x²y² + 2xy + 1 ) = ( x² + 4y² - 5 )² - 4²( xy + 1 )²

                                                            = ( x² + 4y² - 5 )² - ( 4xy + 4 )²

                                                            = [ ( x² + 4y² - 5 ) - ( 4xy + 4 ) ][ ( x² + 4y² - 5 ) + ( 4xy + 4 ) ]

                                                            = ( x² + 4y² - 5 - 4xy - 4 )( x² + 4y² - 5 + 4xy + 4 )

                                                            = [ ( x² - 4xy + 4y² ) - 9 ][ ( x² + 4xy + 4y² ) - 1 ]

                                                            = [ ( x - 2y )² - 3² ][ ( x + 2y )² - 1² ]

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

( a + b )³ - ( a³ + b³ ) = a³ + 3a²b + 3ab² + b³ - a³ - b³

                                  = 3a²b + 3ab²

                                  = 3ab( a + b )

3/    \(x^6-6x^4+12x^2-8\)

\(=\left(x^2\right)^3-3x^22+3x2^2+2^3\)

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

4/   \(\left(x^2+4y^2-5\right)^2-16\left(x^2y^2+2xy+1\right)\)

\(=\left(x^2+4y^2-5\right)^2-4^2\left(xy+1\right)^2\)

\(=\left(x^2-4xy+4y^2-1\right)\left(x^2-4xy+4y^2-9\right)\)

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

a, (\(x\) + y).(\(x\) + y)² - 3\(xy\).(\(x\) + y) 

= (\(x+y\))³ - 3\(x^2\)y - 3\(xy^2\)

= \(x^3\) + 3\(x^2\).y + 3\(xy^2\) + y³ - 3\(x^2\).y  - 3\(xy^2\)

= \(x^3\) + y³ 

b, (\(x-y\)).(\(x-y\))² - 3\(xy\).(\(x-y\)) 

=    (\(x\) - y)³ - 3\(x^2\).y + 3\(xy^2\)

= \(x^3\) - 3\(x^2\)y + 3\(xy^2\) - y³ - 3\(x^2\)y + 3\(xy^2\)

= \(x^3\) - 6\(x^2\)y + 6\(xy^2\) - y³

c, (\(x\) - 2y)² + 4y²

=  \(x^2\) - 4\(xy\) + 4y² + 4y²

=  \(x^2\) - 4\(xy\) + 8y²

a) ( 5x - y )( 25x² + 5xy + y² ) = ( 5x )³ - y³ = 125x³ - y³

b) ( x - 3 )( x² + 3x + 9 ) - ( 54 + x³ ) = x³ - 3³ - 54 - x³ = -27 - 54 = -81

c) ( 2x + y )( 4x² - 2xy + y² ) - ( 2x - y )( 4x² + 2xy + y² ) = ( 2x )³ + y³ - [ ( 2x )³ - y³ ]= 8x³ + y³ - 8x³ + y³ = 2y³

d) ( x + y )² + ( x - y )² + ( x + y )( x - y ) - 3x² = x² + 2xy + y² + x² - 2xy + y² + x² - y² - 3x² = y²

e) ( x - 3 )³ - ( x - 3 )( x² + 3x + 9 ) + 6( x + 1 )²

= x³ - 9x² + 27x - 27 - ( x³ - 3³ ) + 6( x² + 2x + 1 )

= x³ - 9x² + 27x - 27 - x³ + 27 + 6x² + 12x + 6

= -3x² + 39x + 6

= -3( x² - 13x - 2 )

f) ( x + y )( x² - xy + y² ) + ( x - y )( x² + xy + y² ) - 2x³

= x³ + y³ + x³ - y³ - 2x³

= 0

g) x² + 2x( y + 1 ) + y² + 2y + 1

= x² + 2x( y + 1 ) + ( y² + 2y + 1 )

= x² + 2x( y + 1 ) + ( y + 1 )²

= ( x + y + 1 )²

= [ ( x + y ) + 1 ]²

= ( x + y )² + 2( x + y ) + 1

= x² + 2xy + y² + 2x + 2y + 1

`#3107`

`a.`

`4x^2 - 6x = 2x(2x - 3)`

`b.`

`9x^4y^3 + 3x^2y^4 = 3x^2y^2(3x^2y + y^2)`

`c.`

`x^3 - 2x^2 + 5x`

`= x(x^2 - 2x + 5)`

a) 4x² - 6x

= 2x(2x - 3)

b) 9x⁴y³ + 3x²y⁴

= 3x²y³(3x² + 3y)

c) x³ - 2x² + 5x

= x(x² - 2x + 5)

6, x mũ 4 - 4x mũ 3 - 8x mũ 2 + 8x =x (x+2) (x^2-6x+4)

8, x mũ 4 + 2x mũ 3 + x mũ 2 - y mũ 2  = -(y-x^2-x) (y+x^2+x)

10, 4x mũ 2 ( x + y ) -x - y  = (2x-1) (2x+1) (y+x)

Bài 1: 

a) Ta có: \(\left(15x^2\cdot y^2\cdot z\right):3xyz\)

\(=\dfrac{15x^2y^2z}{3xyz}\)

\(=5xy\)

b) Ta có: \(3x^2\cdot\left(5x^2-4x+3\right)\)

\(=3x^2\cdot5x^2-3x^2\cdot4x+3x^2\cdot3\)

\(=15x^4-12x^3+9x^2\)

c) Ta có: \(\left(2x^2-3x\right):\left(x-4\right)\)

\(=\dfrac{2x^2-8x+5x-20+20}{x-4}\)

\(=\dfrac{2x\left(x-4\right)+5\left(x-4\right)+20}{x-4}\)

\(=2x+5+\dfrac{20}{x-4}\)

d) Ta có: \(-5xy\cdot\left(3x^2y-5xy+y^2\right)\)

\(=-5xy\cdot3x^2y+5xy\cdot5xy-5xy\cdot y^2\)

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

a)\(6x-9-x^2\)

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

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

b)\(x^2+4y^2+4xy\)

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

c)\(x^2+8x+16\)

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

d)\(9x^2-12xy+4y^2\)

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

e)\(-25x^2y^2+10xy-1\)

\(=-\left(25x^2y^2-10xy+1\right)\)

\(=-\left(5xy-1\right)^2\)

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

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

j)\(x^2+6x+9\)

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

h)\(9x^2-6x+1\)

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

#H

a, 6x - 9 - x² = - x² + 6x - 9 = - (x² - 6x + 9) = - (x - 3)²

b, x² + 4y² + 4xy = x² + 2. x . 2y + (2y)² = (x + 2y)²

c, x² + 8x + 16 = x² + 2 . x . 4 + 4² = (x + 4)²

d, 9x² - 12xy + 4y² = (3x)² - 2 . 3x . 2y + (2y)² = (3x - 2y)²

e, - 25x²y² + 10xy - 1 = - (25x²y² - 10xy + 1) = - [(5xy)² - 2 . 5xy + 1] = - (5xy - 1)²

f, 4x² - 4x + 1 = (2x)² - 2 . 2x + 1 = (2x - 1)²

j, x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

h, 9x² - 6x + 1 = (3x)² - 2 . 3x + 1 = (3x - 1)²

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

2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)

3. \(16x^2-8x+1=\left(4x-1\right)^2\)

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

5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)

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

7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)

Kết quả nè

1.(x^2-1)^2×(x^2+1)^2

2.(2x-5)^2÷4

3.(4x-1)^2

4.(x+y)^2×(x-y)

5.(1/4x-4/9y)×(1/4x+1/9y)

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

2). (x+5/2)^2

3). {4x-1)^2