xem lại câu a :V

`x^3 -64`

`=x^3 -4^3`

`=(x-4)(x^2 +4.x+4^2)`

`=(x-4)(x^2 +4x+16)`

`27x^3 +1`

`=(3x)^3 +1`

`=(3x+1)[(3x)^2 +3x.1+1^2]`

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

`64m^3 -27`

`=(4m)^3 -3^3`

`=(4m-3)[(4m)^2 -4m.3+3^2]`

`=(4m-3)(16m^2 +12m+9)`

`x^3 +8`

`=x^3 +2^3`

`=(x+2)(x^2 -2.x+2^2)`

`=(x+2)(x^2 -2x+4)`

\(A=1.2+2.3+...+2013.2014\\ \Rightarrow3A=1.2.3+2.3.3+...+2013.2014.3\\ \Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+2013.2014.\left(2015-2012\right)\\ \Rightarrow3A=1.2.3+2.3.4-1.2.3+...+2013.2014.2015-2012.2013.2014\\ \Rightarrow3A=2013.2014.2015\\ \Rightarrow A=\dfrac{2013.2014.2015}{3}\)

hình như sai r

\(B=\dfrac{10x^2-7x-5}{2x-3}\left(ĐKXĐ:x\ne\dfrac{3}{2}\right)\\ =\dfrac{10x^2-15x+8x-12+7}{2x-3}\\ =\dfrac{5x\left(2x-3\right)+4\left(2x-3\right)+7}{2x-3}\\ =\dfrac{\left(2x-3\right)\left(5x+4\right)+7}{2x-3}\\ =5x+4+\dfrac{7}{2x-3}\)

Để `B` nguyên mà `5x+4` nguyên

`=> 7/(2x-3)` nguyên`

`=> 2x-3 in Ư(7)`

`=>2x-3 in {-7;-1;1;7}`

`=> x in {-5;1;2;5}`

Vậy `x in {-5;1;2;5}`

`4m^2 -10m+25`

`=(2m)^2 -2.2m.5+5^2`

`=(2m-5)^2`

`12(2-3b)+35b-9(b+1)`

`=24-36b+35b-9b-9`

`=-10b-15`

thay `b= 1/2` vào biểu thức ta có:

`-10b-15`

`=-10 . 1/2 - 15`

`=-5-15`

`=-20`

`4a-2(10a-1)+8a-2`

`=4a-20a+2+8a-2`

`=-8a`

\(\dfrac{2}{5}+\left(-\dfrac{4}{5}\right)+\left(-\dfrac{1}{2}\right)\\ =\dfrac{-2}{5}+\dfrac{-1}{2}\\ =\dfrac{-4}{10}+\dfrac{-5}{10}\\ =\dfrac{-9}{10}\)