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19 tháng 10 2020

a) 5x3 - 40 = 5( x3 - 8 ) = 5( x - 2 )( x2 + 2x + 4 )

b) x2z + 4xyz + 4y2z = z( x2 + 4xy + 4y2 ) = z( x + 2y )2

c) 4x2 - y2 - 6x + 3y = ( 4x2 - y2 ) - ( 6x - 3y ) = ( 2x - y )( 2x + y ) - 3( 2x - y ) = ( 2x - y )( 2x + y - 3 )

d) x2 + 2x - 4y2 + 1 = ( x2 + 2x + 1 ) - 4y2 = ( x + 1 )2 - ( 2y )2 = ( x - 2y + 1 )( x + 2y + 1 )

e) 3x2 - 3y2 - 12x + 12y = 3( x2 - y2 - 4x + 4y ) = 3[ ( x2 - y2 ) - ( 4x - 4y ) ] = 3[ ( x - y )( x + y ) - 4( x - y ) ] = 3( x - y )( x + y - 4 )

f) x3 + 5x2 + 4x + 20 = x2( x + 5 ) + 4( x + 5 ) = ( x + 5 )( x2 + 4 )

g) x3 - x2 - 25x + 25 = x2( x - 1 ) - 25( x - 1 ) = ( x - 1 )( x2 - 25 ) = ( x - 1 )( x - 5 )( x + 5 )

19 tháng 10 2020

a) \(5x^3-40=5\left(x^3-8\right)=5\left(x-2\right)\left(x^2+2x+4\right)\)

b) \(x^2z+4xyz+4y^2z=z\left(x^2+4xy+4y^2\right)=z\left(x+2y\right)^2\)

c) \(4x^2-y^2-6x+3y=\left(4x^2-y^2\right)-\left(6x-3y\right)\)

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

d) \(x^2+2x-4y^2+1=x^2+2x+1-4y^2\)

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

e) \(3x^2-3y^2-12x+12y=3\left(x^2-y^2-4x+4y\right)\)

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

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

f) \(x^3+5x^2+4x+20=\left(x^3+5x^2\right)+\left(4x+20\right)\)

\(=x^2.\left(x+5\right)+4\left(x+5\right)=\left(x^2+4\right)\left(x+5\right)\)

g) \(x^3-x^2-25x+25=\left(x^3-x^2\right)-\left(25x-25\right)\)

\(=x^2\left(x-1\right)-25\left(x-1\right)=\left(x-1\right)\left(x^2-25\right)\)

\(=\left(x-1\right)\left(x-5\right)\left(x+5\right)\)

12 tháng 8 2021

7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)

8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)

9, ĐK x >= 0 

\(x-2\sqrt{x}-3=x-3\sqrt{x}+\sqrt{x}-3\)

\(=\sqrt{x}\left(\sqrt{x}+1\right)-3\left(\sqrt{x}+1\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)

10, \(-4x^2-4x+10=-\left(4x^2+4x+1\right)+11\)

\(=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)

11;12 xem lại đề

13, \(-x^3+6xy^2-12xy^2+8y^3=-\left(x^3-6xy^2+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)

12 tháng 8 2021

Trả lời:

7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)

8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)

9, \(x-2\sqrt{x}-3\left(ĐK:x\ge0\right)\)

\(=x-3\sqrt{x}+\sqrt{x}-3=\sqrt{x}\left(\sqrt{x}-3\right)+\left(\sqrt{x}-3\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)

10, \(10-4x-4x^2=-\left(4x^2+4x-10\right)=-\left(4x^2+4x+1-11\right)=-\left[\left(2x+1\right)^2-11\right]\)

\(=-\left(2x+1\right)^2+11=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)

11,sửa đề:  \(15x\left(x-3y\right)+20y\left(3y-x\right)=15x\left(x-3y\right)-20y\left(x-3y\right)=5\left(x-3y\right)\left(3x-4y\right)\)

12, \(25x^2-2=\left(5x-\sqrt{2}\right)\left(5x+\sqrt{2}\right)\)

13, sửa đề: \(-x^3+6x^2y-12xy^2+8y^3=-\left(x^3-6x^2y+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)

16 tháng 11 2018

b.10x(x-y)-6y(y-x)=10x(x-y)+6y(x-y)=(10x+6y)(x-y)

16 tháng 11 2018

c.3x2+5y-3xy-5x=(3x2--3xy)-(5x-5y)=3x(x-y)-5(x-y)=(3x-5)(x-y)

8 tháng 9 2020

A = xy + y - 2x - 2

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

= ( x + 1 )( y - 2 )

B = x2 - 3x + xy - 3y

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

= ( x - 3 )( x + y )

C = 3x2 - 3xy - 5x + 5y

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

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

D = xy + 1 + x + y

= y( x + 1 ) + ( x + 1 )

= ( x + 1 )( y + 1 )

E = ax - bx + ab - x2

= ( ax - x2 ) + ( ab - bx )

= x( a - x ) + b( a - x )

= ( a - x )( x + b )

F = x2 + ab + ax + bx

= ( ax + x2 ) + ( ab + bx )

= x( a + x ) + b( a + x )

= ( a + x )( x + b )

G = a3 - a2x - ay + xy

= a2( a - x ) - y( a - x )

= ( a - x )( a2 - y )

Bonus : = ( a - x )[ a2 - ( √y )2 ]

             = ( a - x )( a - √y )( a + √y )

H = 2xy + 3z + 6y + xz

= ( 6y + 2xy ) + ( 3z + xz )

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

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

8 tháng 9 2020

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

B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)

C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)

D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)

E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)

F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)

G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)

H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)

NV
16 tháng 10 2019

\(A=\left(5x\right)^2-1^2=\left(5x-1\right)\left(5x+1\right)\)

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

\(C=x\left(x^2+8x+16\right)=x\left(x+4\right)^2\)

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

\(E=\left(3x\right)^2-\left(y^2-10y+25\right)=\left(3x\right)^2-\left(y-5\right)^2\)

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

\(F=x^2+x+7x+7=x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)

\(G=3x^2+3x-5x-5=3x\left(x+1\right)-5\left(x+1\right)=\left(x+1\right)\left(3x-5\right)\)

\(H=x^2+x-5x-5=x\left(x+1\right)-5\left(x+1\right)=\left(x-5\right)\left(x+1\right)\)

12 tháng 7 2019

a,\(xy+3x-7y-21\)

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

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

12 tháng 7 2019

\(b,2xy-15-6x+5y\)

\(=\left(2xy-6x\right)+\left(-15+5y\right)\)

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

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

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

14 tháng 7 2019

a) \(4x^2-4x+1=\left(2x-1\right)^2\)

14 tháng 7 2019

\(3x\left(x-5\right)-x\left(4+3x\right)=43\)

\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)

\(\Leftrightarrow-19x=43\)

\(\Leftrightarrow x=\frac{-43}{19}\)

25 tháng 8 2017

a) 5x ( x - 2000 ) - x + 2000 = 0

 5x ( x - 2000 ) - ( x - 2000 ) = 0

 5x ( x - 2000 ) = 0

\(\Rightarrow\orbr{\begin{cases}5x=0\\x-2000=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=2000\end{cases}}\)

Vậy .... 

b) x3 - 13x = 0

x ( x2 - 13 ) = 0

x ( x - \(\sqrt{13}\)) - ( x + \(\sqrt{13}\)) = 0

\(\Rightarrow\hept{\begin{cases}x=0\\x-\sqrt{13}\\x+\sqrt{13}\end{cases}}\Rightarrow\hept{\begin{cases}x=0\\x=\sqrt{13}\\x=\sqrt{-13}\end{cases}}\)

Vậy ....

a) x2 + 6 + 9 

= x2 + 2 . 3 . x + 32

= ( x + 3 )2

b) 10x - 25 - x2

= - ( x2 - 10x + 25 )

= - ( x - 5 )2

c) 8x3 - 1/8

= ( 2x )3 - ( 1/2 )3

= ( 2x - 1/2 ) ( 4x2 + x + 1/4 )

d) 1/25 x2 - 64x2

= ( 1/5x )2 - ( 8x )2

= ( 1/5x + 8x ) ( 1/5 - 8x )

30 tháng 9 2018

\(x^3-13x=0\)

<=>  \(x\left(x^2-13\right)=0\)

<=>  \(x\left(x-\sqrt{13}\right)\left(x+\sqrt{13}\right)=0\)

<=>  \(x=0\)

hoặc  \(x-\sqrt{13}=0\)

hoặc  \(x+\sqrt{13}=0\)

<=>  .....