1000 027 = 1000000 + 27 = 100^3 + 3^3 = (100+3)(100^2 - 100.3 + 3^2) 
1000 027 = 103.9709 => 1000 027 là hợp số ( có ít nhất 4 ước 1, 103, 9709, 1000027)

a) \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\)

\(\Leftrightarrow x^3-27+x\left(4-x^2\right)=1\)

\(\Leftrightarrow x^3-27+4x-x^3=1\)

\(\Leftrightarrow4x-27=1\Leftrightarrow4x=28\Leftrightarrow x=7\)

b) \(\left(x-2\right)^3-\left(x-2\right)\left(x^2+2x+4\right)+6\left(x-2\right)\left(x+2\right)=60\)

\(\Leftrightarrow x^3-6x^2+12x+4-x^3-8+6\left(x^2-4\right)=60\)

\(\Leftrightarrow-6x^2+12x-4+6x^2-24=60\)

\(\Leftrightarrow12x-28=60\Leftrightarrow x=\frac{22}{3}\)

a) (x - 3)(x^2 + 3x + 9) + x(x + 2)(2 - x) = 1

x^3 + 3x^2 + 9x - 3x^2 - 9x - 27 + 2x^2 - x^3 + 4x - 2x^2 = 1

4x - 27 = 1

4x = 28

x = 7

b) (x - 2)^3 - (x - 2)(x^2 + 2x + 4) + 6(x - 2)(x + 2) = 60

x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 - x(x^2 + 2x + 4) + 2(x^2 + 2x + 4) + 6x - 24 = 60

x^3 + 12x - 32 - x^2 - 2x^2 - 4x + 2x^2 + 4x + 8 = 60

12x - 24 = 60

12x = 60 + 24

12x = 84

x = 7

Dễ thấy: \(2008^3+1>0\); \(2008^2-2007>0\)

Nên \(\frac{2008^3+1}{2008^2-2007}>0\Leftrightarrow A>0\)

và \(2009-2010< 0\); \(2009^3-1>0\)

\(\Rightarrow\frac{2009^3-1}{2009-2010}< 0\Leftrightarrow B< 0\)

Vậy A > B

a) \(43x^3y^3-32x^2y^2\)

\(=x^2y^2\left(43xy-32\right)\)

b) \(ax-bx+ab-x^2\)

\(=\left(ax+ab\right)-\left(bx+x^2\right)\)

\(=a\left(b+x\right)-x\left(b+x\right)\)

\(=\left(a-x\right)\left(b+x\right)\)

c) \(12a^2b-18ab^2-30b^2\)

\(=6b\left(2a^2-3ab-5b\right)\)

d) \(27a^2\left(b-1\right)-9a^3\left(1-b\right)\)

\(=27a^2\left(b-1\right)+9a^3\left(b-1\right)\)

\(=\left(27a^2+9a^3\right)\left(b-1\right)\)

\(=9a^2\left(b-1\right)\left(a+3\right)\)

a) A = (x + 2y)(x^2 - 2xy + 4y^2) - 8(x^3 + y^3)

A = x(x^2 - 2xy + 4y^2) + 2y(x^2 - 2xy + 4y^2) - 8(x^3 + y^3)

A = x^3 - 2x^2y + 4xy^2 + 2x^2y - 4xy^2 + 8y^3 - 8x^3 - 8y^3

A = -7x^3

b) B = (2x + y)^3 - (8x^3 + y^3) - 2x^2y

B = (2x + y)[(2x)^2 + 2.2xy + y^2] - 8x^3 - y^3 - 2x^2y

B = 2x[(2x)^2 + 2.2xy + y^2] + y[(2x)^2 + 2.2xy + y^3] - 8x^3 - y^3 - 2x^2y

B = 8x^3 + 8x^2y + 2xy^2 + 4x^2y + y^3 - 8x^3 - y^3 - 2x^2y

B = 10x^2y + 6xy^2