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22 tháng 8 2023

1) \(x^2-4xy+4y^2+xz-2yz\)

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

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

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

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

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

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

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

22 tháng 8 2023

mik cảm ơn

31 tháng 7 2021

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

\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)

\(\left(x-y\right)\left(x+y+4\right)\)

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

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

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

\(3,3x^2-4y+4x-3y^2\)

\(3\left(x^2-y^2\right)-4\left(x-y\right)\)

\(3\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\)

\(\left(x-y\right)\left(3x+3y-4\right)\)

\(x^4-6x^3+54x-81\)

\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)

\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)

\(x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)

\(\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)

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

30 tháng 7 2021

\(a,x^2+4x-y^2+4\)

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

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

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

\(b,25-4x^2-4xy-y^2\)

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

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

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

\(c,x^3-x+y^3-y\)

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

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

5 tháng 8 2021

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 )

5 tháng 8 2021

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 ) 

2 tháng 8 2021

Trả lời:

5, x2 - y2 + 4x + 4 

= ( x2 + 4x + 4 ) - y2

= ( x + 2 )2 - y2

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

6, x2 + 2x - 4y2 - 4y

= ( x2 - 4y2 ) + ( 2x - 4y )

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

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

7, 3x2 - 4y + 4x - 3y2

= ( 3x2 - 3y2 ) + ( 4x - 4y )

= 3 ( x2 - y2 ) + 4 ( x - y )

= 3 ( x - y ) ( x + y ) + 4 ( x - y )

= ( x - y ) [ 3 ( x + y ) + 4 ]

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

8, x4 - 6x3 + 54x - 81

= ( x4 - 81 ) - ( 6x3 - 54x )

= ( x2 - 9 ) ( x2 + 9 ) - 6x ( x2 - 9 )

= ( x2 - 9 ) ( x2 + 9 - 6x )

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

= ( x - 3 )3 ( x + 3 )

2 tháng 8 2021

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

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

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

d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)

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

5 tháng 8 2021

a)x²−2x−4y²−4ya)x²-2x-4y²-4y

=x²−2x−4y²−4y+2xy−2xy=x²-2x-4y²-4y+2xy-2xy

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

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

=(x+2y)(x−2y−2)=(x+2y)(x-2y-2)

b)x4+2x³−4x−4b)x4+2x³-4x-4

=x4+2x³+2x²−2x²−4x−4=x4+2x³+2x²-2x²-4x-4

=(x4+2x³+2x²)−(2x²+4x+4)=(x4+2x³+2x²)-(2x²+4x+4)

=x²(x²+2x+2)−2(x²+2x+2)=x²(x²+2x+2)-2(x²+2x+2)

=(x²−2)(x²+2x+2)=(x²-2)(x²+2x+2)

c)x³+2x²y−x−2yc)x³+2x²y-x-2y

=x²(x+2y)−(x+2y)=x²(x+2y)-(x+2y)

=(x²−1)(x+2y)=(x²-1)(x+2y)

=(x+1)(x−1)(x+2y)=(x+1)(x-1)(x+2y)

d)3x²−3y²−2(x−y)²d)3x²-3y²-2(x-y)²

=3(x²−y²)−2(x−y)²=3(x²-y²)-2(x-y)²

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

=(x−y)[3(x+y)−2(x−y)]=(x-y)[3(x+y)-2(x-y)]

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

=(x−y)(x+5y)=(x-y)(x+5y)

e)x³−4x²−9x+36e)x³-4x²-9x+36

=(x³−4x²)−(9x−36)=(x³-4x²)-(9x-36)

=x²(x−4)−9(x−4)=x²(x-4)-9(x-4)

=(x−4)(x²−9)=(x-4)(x²-9)

=(x−4)(x²−3²)=(x-4)(x²-3²)

=(x−4)(x+3)(x−3)=(x-4)(x+3)(x-3)

f)x²−y²−2x−2yf)x²-y²-2x-2y

=(x²−y²)−(2x+2y)=(x²-y²)-(2x+2y)

=(x+y)(x−y)−2(x+y)=(x+y)(x-y)-2(x+y)

=(x+y)(x−y−2)

hok tốt nhé

k đi

30 tháng 7 2021

\(a,x^2+7x+7y-y^2\)

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

\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y+7\right)\)

\(b,x^2-2x-9y^2+6y\)

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

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

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

\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)

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

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

5 tháng 8 2021

Trả lời:

a, 5x2 + 10xy + 5y2 = 5 ( x2 + 2xy + y2 ) = 5 ( x + y )2 

b, x2 + 3x - y2 + 3y = ( x2 - y2 ) + ( 3x + 3y ) = ( x - y )( x + y ) + 3 ( x + y ) = ( x + y )( x - y + 3 )

c, x2 + 5x - y2 + 5y = ( x2 - y2 ) + ( 5x + 5y ) = ( x - y )( x + y ) + 5 ( x + y ) = ( x + y )( x - y + 5 )

d, 3x2 - 3y2 - 2 ( x - y )2 = 3 ( x2 - y2 ) - 2 ( x - y )2 = 3 ( x - y )( x + y ) - 2 ( x - y )2 = ( x - y )[ 3 ( x + y ) - 2 ] = ( x - y )( 3x + 3y - 2 )

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

a) 5x2+10xy+5y2

=5(x2+2xy+y2)

=5(x+y)2

b) x2+3x-y2+3y

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

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

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

c) x2+5x-y2+5y

=(x2-y2)+(5x+5y)

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

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

d) 3x2-3y2-2(x-y)2

=3(x2-y2)-2(x-y)2

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

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

e) x2-2x-4y2-4y

=(x2-4y2)-(2x+4y)

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

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

#H