=(a+b+c)(a2+b2+c2−ab−bc−ca)

=(a+b+c)(a2+2ab+b2−ab−ac+c2)−3ab(a+b+c)

=(a+b)3+c3−3ab(a+b+c)

=a3+3ab(a+b)+b3+c3−3abc−3ab(a+b

a3+b3+c3−3abc

a )   A = - 2 y 3   –   4 .                                       b )   B =   5 x n .

Theo cách mình : 

Bạn chỉ việc chứng minh ƯCLN của nó bằng 1 , rồi suy ra phân số đó tối giảm . 

( Mình nghĩ là như vậy , sai thì thôi nha )

thôi thì cũng cảm ơn bạn

1. 2X-(-8)=-4-(5⁵:5³)

<=> 2X+8=-4-5²

<=>2X+8=-29

<=>2X=-37

=> x=-18,5

2.

2012.2013-1/2012²⁰¹¹

=2012.2013/2012²⁰¹¹-1/2012²⁰¹¹

=2013/2012²⁰¹⁰-1/2012²⁰¹¹

^{khó wá}

(x - 1/2 )(x + 1/2 )(4x - 1)

= ( x 2  + 1/2 x - 1/2 x - 1/4 )(4x - 1)

= ( x 2  - 1/4 )(4x - 1)

= 4 x 3  –  x 2  – x + 1/4

\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right).....\left(1-\dfrac{1}{2008^2}\right)\)

\(=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{2008^2-1}{2008^2}\)

\(=\dfrac{1.3}{4}.\dfrac{2.4}{9}.\dfrac{3.5}{16}....\dfrac{2007.2009}{2008^2}\)

\(=\left(\dfrac{1.2.3...2007}{2.3.4....2008}\right).\dfrac{3.4.5...2009}{2.3.4...2008}\)

\(=\dfrac{1}{2008}.\dfrac{2009}{2}=\dfrac{2009}{4016}\)

=18+5=23

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

\(\left(\dfrac{1}{x}+x-2\right):\left(\dfrac{1}{x^2-x}+1-\dfrac{3}{x-1}\right)\)

\(=\dfrac{x^2-2x+1}{x}:\dfrac{1+x^2-x-3x}{x\left(x-1\right)}\)

\(=\dfrac{\left(x-1\right)^2}{x}\cdot\dfrac{x\left(x-1\right)}{x^2-4x+1}=\dfrac{\left(x-1\right)^3}{x^2-4x+1}\)