a: \(=\dfrac{2x^3+10x^2-31x^2-155x+222x+1110-1170}{x+5}\)

\(=2x^2-31x+222+\dfrac{-1170}{x+5}\)

c: \(=\dfrac{\left(3x-2\right)\left(9x^2+6x+4\right)}{9x^2+6x+4}=3x-2\)

1.

$2x^3-21x^2+67x-60=2x^2(x-5)-11x(x-5)+12(x-5)$

$=(x-5)(2x^2-11x+12)$

$\Rightarrow (2x^3-21x^2+67x-60):(x-5)=2x^2-11x+12$

2.

$x^4+2x^3+x-25=x^2(x^2+5)+2x(x^2+5)-5x^2-9x-25$

$=x^2(x^2+5)+2x(x^2+5)-5(x^2+5)-9x=(x^2+5)(x^2+2x-5)-9x$

$\Rightarrow (x^4+2x^3+x-25):(x^2+5)=x^2+2x-5$ và dư $-9x$

3.

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

$\Rightarrow (27x^3-8):(9x^2+6x+4)=3x-2$

a: \(=8x^3-y^3\)

b: \(=2x^2-3xy+5y^2\)

c: \(=\dfrac{2x^3+10x^2-31x^2-155x+222x+1110-1170}{x+5}\)

\(=2x^2-31x+222+\dfrac{-1170}{x+5}\)

e: \(=\dfrac{\left(3x-2\right)\left(9x^2+6x+4\right)}{9x^2+6x+4}=3x-2\)

Đây bài làm của mình nhé Chúc bạn học tốt

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

\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)

\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)

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

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

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

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

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

những câu khác tương tự

a) (x³ + 8y³) : (2y + x)

= (x + 2y)(x² - 2xy + 4y²) : (2y + x)

= x² - 2xy + 4y²

b) (x³ + 3x²y + 3xy² + y³) : (2x + 2y)

= (x + y)³ : 2(x + y)

= \(\dfrac{\left(x+y\right)^2}{2}\)

c) (6x⁵y² - 9x⁴y³ + 15x³y⁴) : 3x³y²

= 3x³y²(2x² - 3xy + 5y²) : 3x³y²

= 2x² - 3xy + 5y²

a)\(\left(2x-y\right)[\left(2x\right)^2-2.2x.y+y^2]\)

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

b)\(2x^2-3xy+5y^2\)

c)\(2x^3-10x^2-11x^2+55x+12x-60\)

\(=2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\)

\(=\left(x+5\right)\left(2x^2-11x+12\right)\)

\(\Leftrightarrow(2x^3-21x^2+67x-60)/\left(x-5\right)=2x^2-11x+12\)

câu d sai đề rùi đúng là \((x^4+2x^3+10-25)\div\left(x^2+5\right)\)

e)\(27x^3-8=\left(3x\right)^3-2^3=\left(3x-2\right)\left(9x^2+6x+4\right)\)

\(\Leftrightarrow(27x^3-8)\div\left(6x+9x^2+4\right)=3x-2\)