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)

a: \(3xy^2-3x^3-6xy+3x\)

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

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

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

b: \(3x^2+11x+6\)

\(=3x^2+9x+2x+6\)

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

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

c: \(-x^3-4xy^2+4x^2y+16x\)

\(=x\left(-x^2-4y^2+4xy+16\right)\)

\(=x\left\lbrack4^2-\left(x^2-4xy+4y^2\right)\right\rbrack\)

\(=x\cdot\left\lbrack4^2-\left(x-2y\right)^2\right\rbrack\)

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

d: \(xz-x^2-yz+2xy-y^2\)

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

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

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

e: \(4x^2-y^2-6x+3y\)

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

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

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

4x²y-8xy²+18x²y²=2xy(2x-4y+9xy)

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

a) 3xy² - 3x³ - 6xy + 3x 

=3x (y² - x² - 2y +1)

= 3x [ (y-1)² -x² ]

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

b) 3x² +11x+6

= 3 x² +9x +2x +6

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

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

a, 2xy^2 ( x^3 -3xy - 4 )

b, x^2 - 4x - 4x +16

= x(x-4) - 4(x-4)

= (x-4) (x-4)

Lời giải:

a.

$2x^4y^2-6x^2y^3-8xy^2=2xy^2(x^3-3xy-4)$

b. 

$x^2-8x+16=x^2-2.4.x+4^2=(x-4)^2$

c.

$12x^2-12=12(x^2-1)=12(x-1)(x+1)$

d. 

$5x^2y-20xy+20y=5y(x^2-4x+4)=5y(x-2)^2$
e.

$3x^2y^2-27y^2=3y^2(x^2-9)=3y^2(x-3)(x+3)$

f. 

$8x^3-27y^3=(2x)^3-(3y)^3=(2x-3y)(4x^2+6xy+9y^2)$

g.

$4x^4-8x^3+4x^2=(2x^2)^2-2.2x^2.2x+(2x)^2$

$=(2x^2-2x)^2=[2x(x-1)]^2=4x^2(x-1)^2$
h.

$7x^2y^2-28y^4=7y^2(x^2-4y^2)=7y^2(x-2y)(x+2y)$

$

a) 20x²y + 25xy2
= 5xy( 4x + 5y )
b) x² - 5x - 15y - 9y²
= x(x - 5) - 3y(5 + 3y)

\(-8x^2y^2-12xy^2-4xy^2=-8x^2y^2-16xy^2\)

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

-8x²y² - 12xy² - 4xy²

\(=-4xy\left(2xy+3y+y\right)\)

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

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

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

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

\(2x^3y-2xy^3-4xy^2-2xy\)

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

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

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