\(\dfrac{4x +2}{15x^3y}\)  +  \(\dfrac{5y-3}{9x^2y}\)  + \(\dfrac{x +1}{5xy^3}\) 

=\(\dfrac{\left(4x+2\right)\cdot3y^2}{45x^3y^3}\) + \(\dfrac{\left(5y-3\right)\cdot5xy^2}{45x^3y^3}\) + \(\dfrac{\left(x+1\right)\cdot9x^2}{45x^3y^3}\) 

=\(\dfrac{12xy^2+6y^2+25xy^3-15xy^2+9x^3+9x^2}{45x^3y^3}\) 

=\(\dfrac{9x^3+9x^2+25xy^3-3xy^2+6y^2}{45x^3y^3}\)

Đáp án:

 $a.3x³-5x²+7x$

$b.-4x²y-10x²y+2xy$

$c.-x³+2x²+29x+20$

$d.2x⁴-3x³+2x²+3x-4$

$e.x²-4y²$

$h.2x²-6x+13$

$g.3xy⁴-\frac{1}{2}y²+2x²y$ 

$f.-2x²y³+y-3$

Giải thích các bước giải:

 $a.3x.(x²-5x+7)$

$=3x³-5x²+7x$

$b.-2xy.(2x³+5x-1)$

$=-4x⁴y-10xy²+2xy$

$c.(x+4).(-x²+6x+5)$

$=-x³+6x²+5x-4x²+24x+20$

$=-x³+2x²+29x+20$

$d.(x²-1).(2x²-3x+4)$

$=2x⁴-3x³+4x²-2x²+3x-4$

$=2x⁴-3x³+2x2+3x-4$

$e.(x+2y).(x-2y)$

$=x²-\left(2y\right)²$

$=x²-4y²$

$h.(3x-1)²-7(x²+2)$

$=9x²-6x+1-7x²-14$

$=2x²-6x+13$

$g.(6x²$y⁵$-xy³+4x³y²):2xy$

$=3xy⁴-\frac{1}{2}y²+2x²y$ 

$f.(-12x³y⁴+6xy²-18xy):6xy$

$=-2x³y³+y-3$

a.x²-7x+10

⇔x²-2x-5x+10

⇔x(x-2)-5(x-2)

⇔(x-2)(x-5)

b.\(\left(12x^6y^4+9x^5y^3-15x^2y^3\right):3x^2y^3\)

=\(4x^4y+3x^3-5\)

=

x²-7x+10

= x²-5x-2x+10

=x(x-5)-2(x-5)

=(x-5)(x-2)

(12x⁶y⁴+9x⁵y³-15x²y³): 3x²y³

=4x⁴y+3x³-3

a) \(6xy+2y^3-15x-5y^2\)

\(=\left(2y^3-5y^2\right)+\left(6xy-15x\right)\)

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

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

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

a,3x³y³-15x²y²=3x²y²(xy-5)

b,2x(x-5y)+8y(5y-x)=2x(x-5y)-8y(x-5y)=(x-5y).(2x-8y)

c,(3x-1)²-16=(3x-1)²-4²=(3x-1+4)(3x-1-4)=(3x+3)(3x-5)

d,x³-3x²+3x-1=x³-1-(3x²+3x)=x³-1-3x(x+1)=(x³-1-3x)(x+1)

e,125x³+1=(5x)³+1³=(5x+1)(25x²-5x.1+1²)

f,x³+6x²y+12xy²+8y³=x³+3.x².2y+3.x.(2y)²+(2y)³=(x+2y)³

a) 3x(x + 1) - 5y(x + 1)

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

b) 3x(x - 6) - 2(x - 6)

= (x - 6)(3x - 2)

c) 4y(x - 1) - (1 - x)

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

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

d) (x - 3)³ + 3 - x

= (x - 3)³ - (x - 3)

= (x - 3)[(x - 3)² - 1]

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

= (x - 3)(x - 4)(x - 2)

e) 7x(x - y) - (y - x)

= 7x(x - y) + (x - y)

= (x - y)(7x + 1)

h) 3x³(2y - 3z) - 15x(2y - 3z)²

= (2y - 3z)[3x³ - 15x(2y - 3x)]

= 3x(2y - 3x)[x² - 5(2y - 3x)]

= 3x(2y - 3x)(x² - 10y + 3x)

= 3x(2y - 3x)(x² + 3x - 10y)

k) 3x(x + 2) + 5(-x - 2)

= 3x(x + 2) - 5(x + 2)

= (x + 2)(3x - 5)

l) 18x²(3 + x) + 3(x + 3)

= (x + 3)(18x² + 3)

= 3(x + 3)(6x² + 1)

m) 7x(x - y) - (y - x)

= 7x(x - y) + (x - y)

= (x - y)(7x + 1)

n) 10x(x - y) - 8y(y - x)

= 10x(x - y) + 8y(x - y)

= (x - y)(10x + 8y)

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

Bài 2: 

a: \(=x^{n+19-14}=x^{n+5}\)

b: \(=x^{94-17-65}=x^{12}\)