b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)

\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)

\(=\dfrac{2y^2+8y+12}{y-1}\)

Bài 2: 

a: \(3\left(x-1\right)\left(x^2+x+1\right)+\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)\)

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

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

\(=-3x^2+7x-4\)

\(=-3\cdot\left(-1\right)^2+7\cdot\left(-1\right)-4\)

=-3-4-7=-14

b: \(=27x^3y^3-8-3xy\left(9x^2y^2+6xy+1\right)\)

\(=27x^3y^3-8-27x^3y^3-18x^2y^2-3xy\)

\(=-18x^2y^2-3xy-8\)

\(=-18\cdot\left[\left(-2010\right)\cdot\left(-\dfrac{1}{2010}\right)\right]^2-3\cdot\left(-2010\right)\cdot\dfrac{-1}{2010}-8\)

\(=-18-3-8=-29\)

A = 5x(x - y) - y(5x - y)

A = 5x² - 5xy - 5xy + y²

A = 5x² - 10xy + y² (1)

Thay x = -1; y = 3 vào (1), ta có:

5.(-1)² - 10.(-1).3 + 3² = 44

B = 4y(x² - 3xy + 3y²) - 2xy(2x - 6y - 3)

B = 4x²y - 12x² + 12y³ - 4x²y + 12xy² + 6xy

B = 12y³ + 6xy (1)

Thay x = 5; y = -1 vào (1), ta có:

12.(-1)³ + 6.5.(-1) = -42

C = 5x²(x - y²) + 3x(xy² - y) - 5x³ 

C = 5x³ - 5x²y² + 3x²y² - 3xy - 5x³ 

C = -2x²y² - 3xy (1)

Thay x = -2; y = -5 vào (1), ta có:

-2.(-2)².(-5)² - 3.(-2).(-5) = -230

D = 6x²(y² - xy + 2x²y) - 3xy(2xy - x² + 4x³)

D = 6x²y² - 6x³y + 12x⁴y - 6x²y² + 3x³y - 12x⁴y

D = -3x³y (1)

Thay x = 11; y = -1 vào (1), ta có:

-3.11³.(-1) = 3993

a)P= 15+45x+33x^2-55x^3

a: \(P=\left(5x-1-5x-4\right)^2=\left(-3\right)^2=9\)

b: \(Q=\left(x+y\right)^3-3xy\left(x+y\right)=x^3+y^3\)

c: \(=\dfrac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{5^{32}-1}{2}\)

\(a,\Leftrightarrow\left\{{}\begin{matrix}5x+15y=-10\\5x-4y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}19y=-21\\5x-4y=11\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{21}{19}\\5x-4\left(-\dfrac{21}{19}\right)=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{25}{19}\\y=-\dfrac{21}{19}\end{matrix}\right.\)

\(c,\Leftrightarrow\left\{{}\begin{matrix}3x+5y=1\\10x-5y=-40\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+5y=1\\13x=-39\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=2\end{matrix}\right.\\ d,\Leftrightarrow\left\{{}\begin{matrix}5x-10y=-30\\5x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x-3y=5\\-7y=-35\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=5\end{matrix}\right.\\ e,\Leftrightarrow\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\2\left(x+y\right)+4\left(x-y\right)=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y=6\\2\left(x+y\right)+3\cdot6=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-y=6\\x+y=-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\y=-\dfrac{13}{2}\end{matrix}\right.\)

13: =x(a^3-1)-b(a-1)

=x(a-1)(a^2+a+1)-b(a-1)

=(a-1)(a^2x+a*x+x-b)

12: =(x-y)(x+y)-(x-y)

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

10: =3(x^2-4y^2)

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

7: =x^2-x-5x+5=(x-1)(x-5)

8: =x^2+3x+4x+12=(x+3)(x+4)

9: =2x^2-6x-x+3=(x-3)(2x-1)

a) \(\left(x+2\right)\left(x^2-24+4\right)\left(x^3+8\right)\)

\(=\left(x+2\right)\left(x^2-20\right)\left(x^3+8\right)\)

\(=\left(x^3-20x+2x^2-40\right)\left(x^3+8\right)\)

\(=x^6+8x^3-20x^4+160x+2x^5+16x^2-40x^3-120\)

\(=x^6+2x^5-20x^4-32x^3+16x^2+160x-120\)

b) \(\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)

\(=8x^3+2x^2+\dfrac{1}{2}x-2x^2-\dfrac{1}{2}x-\dfrac{1}{8}\)

\(=8x^3-\dfrac{1}{8}\)

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

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

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

\(=2x^4\)

d) \(\left(x+3\right)\left(x^2-3x+9\right)-x^3\)

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

\(=x^3+3^3-x^3\)

\(=27\)

e) \(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-26x^3\)

\(=\left(3x+y\right)\left[\left(3x\right)^2-3x\cdot y+y^2\right]-26x^3\)

\(=\left(3x\right)^3+y^3-26x^3\)

\(=27x^3+y^3-26x^3\)

\(=x^3+y^3\)

g) \(\left(x+3y\right)\left(x^2-3xy+9y^2\right)+\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)

\(=\left(x+3y\right)\left[x^2-x\cdot3y+\left(3y\right)^2\right]+\left(3x-y\right)\left[\left(3x\right)^2+3x\cdot y+y^2\right]\)

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

\(=x^3+27y^3+27x^3-y^3\)

\(=28x^3+26y^3\)

Yêu cầu của đề là gì ?

a) Sửa đề:

(x + 2)(x² - 2x + 4)(x³ + 8)

= (x³ + 8)(x³ + 8)

= (x³ + 8)²

b) (2x - 1/2)(4x² + x + 1/4)

= (2x)³ - (1/2)³

= 8x³ - 1/8

c) (x² + y)(x² - y) + y² + x⁴

= (x²)² - y² + y² + x⁴

= 2x⁴

d) (x + 3)(x² - 3x + 9) - x³

= x³ + 3³ - x³

= 27

e) (3x + y)(9x² - 3xy + y²) - 26x³

= (3x)³ + y³ - 26x³

= 27x³ + y³ - 26x³

= x³ + y³

g) (x + 3y)(x² - 3xy + 9y²) + (3x - y)(9x² + 3xy + y²)

= x³ + (3y)³ + (3x)³ - y³

= x³ + 27y³ + 27x³ - y³

= 28x³ + 26y³