a) ( 3x - 2 )( 4x + 5 ) - 6x( 2x - 1 )

= 12x² + 7x - 10 - 12x² + 6x

= 13x - 10

b) ( 2x - 5 )² - 4( x + 3 )( x - 3 )

= 4x² - 20x + 25 - 4( x² - 9 )

= 4x² - 20x + 25 - 4x² + 36

= 61 - 20x

c) 2x³ - 5x² + 7x - 6

= 2x³ - 3x² - 2x² + 3x + 4x - 6

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

= ( 2x - 3 )( x² - x + 2 )

=> ( 2x³ - 5x² + 7x - 6 ) : ( 2x - 3 ) = x² - x + 2

a, (3x - 2 ) (4x + 5) - 6x (2x -1) = ( 7x + 15x -8x - 10 ) - ( 12x² -6x ) = 7x² + 15x - 8x -10 -12x² + 6x = -5x² + x - 10 

Giải

1) 3xy² : 5x = \(\frac{3}{5}\)y²

2) 15x⁴yz³ : 4xyz = \(\frac{15}{4}\)x³z²

3) (4x²y² - 12xy³ - 7x) : 3x = \(\frac{4}{3}\)xy² - 4y³ - \(\frac{7}{3}\)

4) (14x⁴y² - 12xy³ - x) : 4x = \(\frac{7}{2}\)x³y² - 3y³ - \(\frac{1}{4}\)

5) (6x² + 13x - 5) : (2x + 5) = (3x - 1)(2x + 5) : (2x + 5) = 3x - 1

6) (2x⁴ + x³ - 5x² - 3x - 3) : (x² - 3)
= 2x⁴ + x² - 6x² + x³ - 3 - 3x : x² - 3
= x²(2x² + x + 1) - 3(2x² + x + 1) : x² - 3
= (2x² + x + 1)(x² - 3) : x² - 3

= 2x² + x + 1

a: =-1/5x^5y^2

b: =-9/7xy^3

c: =7/12xy^2z

d: =2x^4

e: =3/4x^5y

f: =11x^2y^5+x^6

Đáp án:

 $a.3x³-5x²+7x$

$b.-4x²y-10x²y+2xy$

$c.-x³+2x²+29x+20$

$d.2x⁴-3x³+2x²+3x-4$

$e.x²-4y²$

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

#Học tốt!!!

a) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}=\dfrac{15x.2y^2}{7y^3.x^2}=\dfrac{30}{7xy}\)

b) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)=\dfrac{-4y^2.3x^2}{11x^4.8y}=\dfrac{-3y}{22x^2}\)

c) \(\dfrac{x^3-8}{5x+20}.\dfrac{x^2+4x}{x^2+2x+4}\\ =\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{5\left(x+4\right)}.\dfrac{x\left(x+4\right)}{x^2+2x+4}\\ =\dfrac{x^2-2x}{5}\)