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29 tháng 11 2023

a: \(x^4-2x^3+x^2-2x\)

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

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

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

b: \(x^4+x^3-8x-8\)

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

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

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

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

29 tháng 10 2021

Bài 1: 

b: \(3x-6=x^2-16\)

\(\Leftrightarrow x^2-3x-10=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

a: =64x^4+16x^2y^2+y^4-16x^2y^2

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

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

b: =x^8+2x^4+1-x^4

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

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

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

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

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

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

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

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

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

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

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

30 tháng 9 2019

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

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

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

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

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

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

=x^4-(x-1)^2

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

MIK KO BIT DUNG HAY KO CON B THI MIK KO BIET LAM

30 tháng 9 2019

Câu b dễ thôi

\(x^4-4x^3-8x^2+8x\)

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

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

30 tháng 9 2021

a) \(=\left(x^2-6\right)\left(x^2-1\right)=\left(x^2-6\right)\left(x-1\right)\left(x+1\right)\)

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

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

30 tháng 9 2021

cảm ơn

 

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)

19 tháng 9 2018

A = 6x4 - 5x3 + 4x2 + 2x - 1

   = 6x4 + 3x3 - 8x3 - 4x2 + 8x2 + 4x - 2x - 1

   = 3x3. ( 2x + 1 ) - 4x2 ( 2x + 1 ) + 4x ( 2x + 1 ) - ( 2x + 1 )

   = ( 2x + 1 ) ( 3x3 - 4x2 + 4x - 1 )

    = ( 2x + 1 ) ( 3x3 - x2 - 3x2 + x + 3x - 1 )

     = ( 2x + 1 ) [ x2 ( 3x - 1 ) - x ( 3x - 1 ) + ( 3x - 1 ) ]

     = ( 2x + 1 ) ( 3x - 1 ) ( x2 - x + 1 )

B = 4x4 + 4x3 + 5x2 + 8x - 6

    = 4x4 - 2x3 + 6x3 - 3x2 + 8x2 - 4x + 12x - 6

     = 2x3 ( 2x - 1 ) + 3x( 2x - 1 ) + 4x ( 2x - 1 ) + 6 ( 2x - 1 )

     = ( 2x - 1 ) ( 2x3 + 3x2 + 4x + 6 )

     = ( 2x - 1 ) [ x2 ( 2x + 3 ) + 2 ( 2x + 3 ) ]

      = ( 2x - 1 ) ( 2x + 3 ) ( x2 + 2 )

C = x4 + x3 - 5x2 + x - 6

   = x4 - 2x3 + 3x3 - 6x2 + x2 - 2x + 3x - 6 

   = x3 ( x - 2 ) + 3x2 ( x - 2 ) + x ( x - 2 ) + 3 ( x - 2 )

   = ( x - 2 ) ( x3 + 3x2 + x + 3 )

    = ( x - 2 ) [ x2 ( x + 3 ) + ( x + 3 ) ]

    = ( x - 2 ) ( x + 3 ) ( x2 + 1 ) 

25 tháng 8 2023

\(b,x^3-2x^2-4xy^2+x\)

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

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

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

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

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

\(---\)

\(c,\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8\)

\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-8\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\) (1)

Đặt \(y=x^2+7x+10\), thay vào (1) ta được:

\(y\left(y+2\right)-8\)

\(=y^2+2y+1-9\)

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

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

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

\(=\left(x^2+7x+10-2\right)\left(x^2+7x+10+4\right)\)

\(=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)

#Ayumu

2 tháng 8 2021

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

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

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

d, \(x^3-4x^2-8x+8=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)=\left(x^2-6x+4\right)\left(x+2\right)\)

2 tháng 8 2021

Trả lời:

1, x2 - 4 - 3 ( x - 2 )

= ( x2 - 4 ) - 3 ( x - 2 )

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

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

= ( x - 2 ) ( x - 1 )

2, x2 - xy + 5y - 25

= ( x2 - 25 ) - ( xy - 5y )

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

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

3, x3 + x2 - 2x - 8

= ( x3 - 8 ) + ( x2 - 2x )

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

= ( x - 2 ) ( x2 + 2x + 4 + x )

= ( x - 2 ) ( x2 + 3x + 4 )

4, x3 - 4x2 - 8x + 8 

= ( x3 + 8 ) - ( 4x2 + 8x )

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

= ( x + 2 ) ( x2 - 2x + 4 - 4x )

= ( x + 2 ) ( x2 - 6x + 4 )