1) \(4x^5y^2-8x^4y^2+4x^3y^2\)

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

\(=4x^3y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

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

2) \(5x^4y^2-10x^3y^2+5x^2y^2\)

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

\(=5x^2y^2\left(x^2-2\cdot x\cdot1+1^2\right)\)

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

3) \(12x^2-12xy+3y^2\)

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

\(=3\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

4) \(8x^3-8x^2y+2xy^2\)

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

\(=2x\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

5) \(20x^4y^2-20x^3y^3+5x^2y^4\)

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

\(=5x^2y^2\left[\left(2x\right)^2-2\cdot2x\cdot y+y^2\right]\)

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

1: 4x^5y^2-8x^4y^2+4x^3y^2

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

=4x^3y^2(x-1)^2

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

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

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

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

a) (25x^5 – 5x^4 + 10x^2) : 5x^2

= (25x^5 : 5x^2) – (5x^4 : 5x^2) + (10x^2 : 5x^2)

= 5x^3 – x^2 + 2

b) (15x^3y^2- 6x^2y – 3x^2y^2) : 6x^2y

= (15x^3y^2 : 6x^2y) + (-6x^2y : 6x^2y) + (- 3x^2y^2 : 6x^2y)

=\(\frac{15}{6}xy-1-\frac{3}{6}y\)

=\(\frac{5}{2}xy-1-\frac{1}{2}y\)

a) (25x⁵ – 5x⁴ + 10x²) : 5x² = (25x⁵ : 5x² ) - (5x⁴ : 5x² ) + (10x² : 5x² )

= 5x³ – x² + 2

b) (15x³y² – 6x²y – 3x²y²) : 6x²y

= (15x³y² : 6x²y) + (– 6x²y : 6x²y) + (– 3x²y² : 6x²y)

= \(\dfrac{15}{6}\)xy - 1 - \(\dfrac{3}{6}\)y = \(\dfrac{5}{2}\)xy - \(\dfrac{1}{2}\)y - 1.

6) \(9x^3y^2+3x^2y^2=3x^2y^2\left(3x+1\right)\)

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

8) \(6x^2y+4xy^2+2xy=2xy\left(3x+2y+1\right)\)

9) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=5x\left(x-2y\right)\left(x-3\right)\)

10) \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(3+5x\right)\)

6) 9x³y² + 3x²y² = 3x²y²( 3x + 1 )

7) x³ + 2x² + 3x = x( x² + 2x + 3 )

8) 6x²y + 4xy² + 2xy = 2xy( 3x + 2y + 1 )

9) 5x²( x - 2y ) - 15x( x - 2y ) = 5x( x - 2y )( x - 3 )

10 3( x - y ) - 5x( y - x ) = 3( x - y ) + 5x( x - y ) = ( x - y )( 3 + 5x )

a: =-2/5x^5y^7

Hệ số: -2/5

bậc: 12

b: =3/4*x^2y^3*12/5x^4=9/5x^6y^3

Hệ số: 9/5

bậc: 9

c: =4/9x^6y^6

hệ số: 4/9

bậc: 12

d: =2/5x^6y^6

hệ số: 2/5

bậc: 12

a) (x + 3y) (2x²y - 6xy²)

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

= 2xy [(x + 3y) (x - 3y)]

= 2xy (x² - 3y²)

b) (6x⁵y² - 9x⁴y³ + 15x³y⁴) : 3x³y²

= (6x⁵y² : 3x³y²) + (-9x⁴y³ : 3x³y²) + (15x³y⁴ : 3x³y²)

= [(6 : 3) (x⁵ : x³) (y² : y²)] + [(-9 : 3) (x⁴ : x³) (y³ : y²)] + [(15 : 3) (x³ : x³) (y⁴ : y²)]

= 2x² + (-3xy) + 5y²

= 2x² - 3xy + 5y²