Đề bài là gì sao không ghi rõ?? 

a) Xem lại đề

b) x³ - 4x²y + 4xy² - 9x

= x(x² - 4xy + 4y² - 9)

= x[(x² - 4xy + 4y² - 3²]

= x[(x - 2y)² - 3²]

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

c) x³ - y³ + x - y

= (x³ - y³) + (x - y)

= (x - y)(x² + xy + y²) + (x - y)

= (x - y)(x² + xy + y² + 1)

d) 4x² - 4xy + 2x - y + y²

= (4x² - 4xy + y²) + (2x - y)

= (2x - y)² + (2x - y)

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

e) 9x² - 3x + 2y - 4y²

= (9x² - 4y²) - (3x - 2y)

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

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

f) 3x² - 6xy + 3y² - 5x + 5y

= (3x² - 6xy + 3y²) - (5x - 5y)

= 3(x² - 2xy + y²) - 5(x - y)

= 3(x - y)² - 5(x - y)

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

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

a: 2x^2y-50xy=2xy(x-25)

b: 5x^2-10x=5x(x-2)

c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)

d: \(x^2-xy+x=x\left(x-y+1\right)\)

e: x(x-y)-2(y-x)

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

=(x-y)(x+2)

f: 4x^2-4xy-8y^2

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

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

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

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

f1: x^2ỹ-y^2+y

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

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

https://olm.vn/hoi-dap/detail/88061957704.html bạn tham khảo câu hỏi này 

a) \(x^2+5y^2+2x-4xy-10y+14\)

\(=\left(x^2-4xy+4y^2\right)+\left(2x-4y\right)+1+\left(y^2-6y+9\right)+4\)

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

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

Vì \(\left(x-2y+1\right)^2\ge0\)

      \(\left(y-3\right)^2\ge0\)

 \(\Rightarrow\left(x-2y+1\right)^2+\left(y-3\right)^2+4\ge4>0\)với mọi x,y (ĐPCM)
b) \(5x^2+10y^2-6xy-4x-2y+3\)

\(=\left(4x^2-4x+1\right)+\left(x^2-6xy+9y^2\right)+\left(y^2-2y+1\right)+1\)

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

Vì \(\left(2x-1\right)^2\ge0\)

      \(\left(x-3y\right)^2\ge0\)

       \(\left(y-1\right)^2\ge0\)

 \(\Rightarrow\left(2x-1\right)^2+\left(x-3y\right)^2+\left(y-1\right)^2+1\ge1>0\)vợi mọi x,y (ĐPCM)

c: Ta có: \(-2xy-3x^2y^2\)

\(=-2xy-3xy\cdot xy\)

\(=-xy\left(2+3xy\right)\)

a: Ta có: \(5x^2-4xy-x^2y\)

\(=x\left(5x-4y-xy\right)\)

a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)

b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)

c) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5}{3}\left(x\ne y\right)\)

d) \(\dfrac{x^2-y^2}{x+y}=x-y\left(đk:x\ne-y\right)\)

e) \(\dfrac{x^3-x^2+x-1}{x^2-1}=\dfrac{x^2+1}{x+1}\left(đk:x\ne\pm1\right)\)

f) \(\dfrac{x^2+4x+4}{2x+4}=\dfrac{x+2}{2}\left(đk:x\ne-2\right)\)

D= 5x^2+8xy+5y^2-2x+2y  

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

=(2x+2y)^2+x^2-2*1/2x+1/4+y^2+2*1/2y+1/4-1/2

(2x+2y)^2+(x-1/2)^2+(y+1/2)^2-1/2>=-1/2

suy ra D>=-1/2 nên D có GTNN là -1/2

Ta có : 5D = 25x² + 40xy + 25y² - 10x + 10y

5D = (5x+ 4y - 1)² + 9y² + 18y - 1  

5D = ( 5x + 4y - 1)² + 9 (y + 1)² - 2

D =\(\frac{1}{5}\). ( 5x + 4y - 1)² + \(\frac{9}{5}\).( y + 1)²  -  \(\frac{2}{5}\)  \(\ge\)\(\frac{-2}{5}\)

Dấu "=" xảy ra khi y+1 = 0  \(\Leftrightarrow\)y = -1

                          5x + 4y - 1 = 0  \(\Leftrightarrow\)x=1

Vậy GTNN của D = \(\frac{-2}{5}\)khi x = 1 ; y = -1

Ta có: 2E = 4x² + 8y² - 8xy - 8x - 8y + 4006

2E = ( 4y - x - 1)² + x² - 6x + 4003

2E = ( 4y - x - 1)² + ( x - 3)² + 4003 - 9

E = \(\frac{1}{2}\).( 4y - x - 1)² +\(\frac{1}{2}\).( x - 3 )² + 1997 \(\ge\)1997

Dấu "=" xảy ra khi x - 3 = 0  \(\Leftrightarrow\)x = 3

                            4x - x -1 = 0  \(\Leftrightarrow\)y = 1

Vậy GTNN của E = 1997 khi x = 3 ; y = 1