1) x³ + 2x² + x

= x(x² + 2x + 1)

= x(x + 1)²

2) 5x³ - 10x² + 5x

= 5x(x² - 2x + 1)

= 5x(x - 1)²

3) 8x²y - 8xy + 2x

= 2x(4xy - 4y + 1)

5) 2x² + 5x³ + x²y

= x²(2 + 5x + y)

6) 4x²y - 8xy² + 18x²y²

= 2xy(2x - 4y + 9xy) 

  Chúc Bạn Học Tốt !

a) 20x - 5y

= 5(4x - y)

b) 5x(x - 1)- 3x(x - 1)

= 2x(x - 1)

c) x(x + y) - 6x - 6y

= x(x + y) - (6x + 6y)

= x(x + y) - 6(x + y)

= (x + y)(x - 6)

d) 6x³ - 9x²

= 3x²(2x - 3)

e) 4x²y - 8xy² + 10x²y²

= 2xy(2x - 4y + 5xy)

g) 20x²y - 12x³

= 4x²(5y - 3x)

h) 8x⁴ + 12x²y⁴ - 16x³y⁴

= 4x²(2x² + 3y⁴ - 4xy⁴)

k) 4xy² + 8xyz

= 4xy(y + 2z)

giúp mình vs ạ c ơn nhiều

a, \(x^4+2x^2+1-x^2\)

= \(\left(x^2+1\right)^2-x^2\)

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

b, \(x^4+x^2+1\)

= \(x^4+2x^2+1-x^2\)

= .. ( như phần a )

c, \(y^4+64\)

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

d, \(4xy+3z-12y-xz\)

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

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

e, \(x^2-4xy+4y^2-z^2+6z-9\)

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

g, \(x^2-4xy+5x+4y^2-10y\)

\(=\left(x^2-4xy+4y^2\right)+\left(5x-10y\right)\)

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

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

h, \(x^2-7x+6\)

\(=x^2-6x-x+6\)

\(=x\left(x-6\right)-\left(x-6\right)\)

\(=\left(x-6\right)\left(x-1\right)\)

i, \(x^3+5x^2+6x+2\)

\(=x^3+x^2+4x^2+4x+2x+2\)

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

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

phần b là 6^4 nhé

where is đề

a) 20x-5y=5(4x-y)

b) 5x(x-1)-3x(x-1)=(5x-3x)(x-1)=2x(x-1)

c) x(x+y)-6x-6y=x(x+y)-(6x+6y)=x(x+y)-6(x+y)=(x-6)(x+y)

d) 6x³-9x²=3x²(2x-3)

e) 4x²y - 8xy² + 10x²y²=2xy(2x-4y+5xy)

g) 20x²y-12x³=4x²(5y-3x)

h) 8x⁴+ 12x²y⁴- 16x³y⁴ = 4x²(2x²+3y⁴-4xy⁴)

k) 4xy² + 8xyz=4xy(y+2z)

l) 3x(x + 1) - 5y( x + 1 )=(x+1)(3x-5y)

m) 4x²-1=(2x-1)(2x+1)

o) 9-(x-y)²=(3-x+y)(3+x-y)

p) x³+27=(x+3)(x²+3x+9)

n) (x-y)²-4=(x-y-2)(x-y+2)

r) x⁴ + 2x² + 1=(x⁴+x²)+(x²+1)=x²(x²+1)+(x²+1)=(x²+1)²

s) 4x²  - 12xy + 9y²  = (2x-3y)²

t) x² - x - y² - y =(x²-y²)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)

v) x³ - x + y³ - y = (x³+y³)-(x+y)=(x+y)(x²-xy+y²)-(x+y)=(x+y)(x²-xy+y²-1)

4x²y-8xy²+18x²y²=2xy(2x-4y+9xy)

\(4x^2y-8xy^2+18x^2y^2=2xy\left(2x-4y+9xy\right)\)

\(a,0,5x^3+4x^2y+0,5xy^2\\ =0,5x\left(x^2+8xy+y^2\right)\\ b,0,25x^9\left(y-1\right)+0,75y\left(1-y\right)\\ =0,25x^9\left(y-1\right)-0,75y\left(y-1\right)=\left(y-1\right)\left(0,25x^9-0,75y\right)\\ c,0,25x^2-0,5xy+0,25y^2-0,25\\ =\left(0,5x-0,5y\right)^2-0,25\\ =\left(0,5x-0,5y-0,5\right)\left(0,5x-0,5y+0,5\right)\\ =0,25\left(x-y-1\right)\left(x-y+1\right)\)

Các câu sau tương tự

a: Ta có: \(-x^2+2xy-4y^2+2x+10y-8\)

\(=-x^2+2xy-y^2+2x-2y-3y^2+12y-8\)

\(=-\left(x-y\right)^2+2\left(x-y\right)-1-3y^2+12y-12+5\)

\(=-\left(x-y-1\right)^2-3\left(y^2-4y+4\right)+5=-\left(x-y-1\right)^2-3\left(y-2\right)^2+5\le5\forall x,y\)

Dấu '=' xảy ra khi x-y-1=0 và y-2=0

=>y=2 và x=y+1=2+1=3

b: \(-x^2-y^2+xy+x+y\)

\(=-\frac14\left(4x^2+4y^2-4xy-4x-4y\right)\)

\(=-\frac14\left\lbrack4x^2-4xy+y^2-4x+2y+3y^2-6y\right\rbrack\)

\(=-\frac14\left\lbrack\left(2x-y\right)^2-2\left(2x-y\right)+1+3y^2-6y+3-4\right\rbrack\)

\(=-\frac14\cdot\left\lbrack\left(2x-y-1\right)^2+3\left(y-1\right)^2-4\right\rbrack=-\frac14\left(2x-y-1\right)^2-\frac34\left(y-1\right)^2+1\le1\forall x,y\)

Dấu '=' xảy ra khi y-1=0 và 2x-y-1=0

=>y=1 và 2x=y+1=1+1=2

=>y=1 và x=1

Phân tích đa thức thành nhân tử

1: \(x^2-x-y^2-y\)

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

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

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

2: \(x^2-y^2+x-y\)

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

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

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

3: \(3x-3y+x^2-y^2\)

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

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

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

4: \(5x-5y+x^2-y^2\)

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

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

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

5: \(x^2-5x-y^2-5y\)

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

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

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

6: \(x^2-y^2+2x-2y\)

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

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

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

7: \(x^2-4y^2+x+2y\)

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

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

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

8: \(x^2-y^2-2x-2y\)

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

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

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

9: \(x^2-4y^2+2x+4y\)

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

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

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

d) \(4x^2y^2-8xy^2+4y^2=4y^2\left(x^2-2x+1\right)=4y^2\left(x-1\right)^2\)

e) \(x^3y+10x^2y+35xy=xy\left(x^2+10x+35\right)\)

f) \(2x^3-4x^2y+2xy^2-8x=2x\left(x^2-2xy+y^2-4\right)=2x\left[\left(x-y\right)^2-4\right]=2x\left(x-y-2\right)\left(x-y+2\right)\)

g) \(3x^2-9xy-6x+18y=3x\left(x-3y\right)-6\left(x-3y\right)=3\left(x-3y\right)\left(x-2\right)\)

h) \(x^2y^2-3xy^2+2xy-6y=xy\left(xy+2\right)-3y\left(xy+2\right)=\left(xy+2\right)\left(xy-3y\right)=y\left(xy+2\right)\left(x-3\right)\)

d: \(4x^2y^2-8xy^2+4y^2\)

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

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

e: \(x^3y+10x^2y+35xy\)

\(=xy\left(x^2+10x+35\right)\)

f: \(2x^3-4x^2y+2xy^2-8x\)

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

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