`-9 1/3*5/9+(-9 1/3)*4/9-0,5`

`=-9 1/3*(5/9+4/9)-0,5`

`=-9 1/3-0,5`

`=-59/6`

`(0,7+3 1/5):1/8+75%`

`=39/10*8+3/4`

`=156/5+3/4=639/20`

`(4-5/12):3+7/36`

`=43/12:3+7/36`

`=43/36+7/36`

`=50/36=25/18`

`1,25:15/20+(25%-5/6):4 2/3`

`=5/3+(1/4-5/6):14/3`

`=5/3-7/12:14/3`

`=5/3-1/8=37/24`

`a)55^{n+1}-55^n`

`=55^n(55-1)=54.55^n\vdots 54AAn\inZZ`

`b)n^2(n+1)+2n(n+1)`

`=(n+1)(n^2+2n)`

`=n(n+1)(n+2)`

Vì `n(n+1)(n+2)` là tích 3 số nguyên liên  tiếp

`=>n(n+1)(n+2)\vdots 6AAn\inZZ`

`c)(2n-1)^3-(2n-1)`

`=(2n-1)[(2n-1)^2-1]`

`=(2n-1)(2n-1-1)(2n-1+1)`

`=2n(2n-2)(2n-1)`

`=4n(n-1)(2n-1)`

Vì `n(n-1)` là tích 2 số nguyên liên tiếp

`=>n(n-1)\vdots 2AAn\inZZ`

`=>4n(n-1)(2n-1)\vdots 8AAn\inZZ`

`=>dpcm`

`a)x^2+x=0`

`<=>x(x+1)=0`

`<=>[(x=0),(x=-1):}`

`b)x(x-3)+4x-12=0`

`<=>x(x-3)+4(x-3)=0`

`<=>(x-3)(x+4)=0`

`<=>[(x=3),(x=-4):}`

`c)2x(x-2)+3(x-2)=0`

`<=>(x-2)(2x+3)=0`

`<=>[(x=2),(x=-3/2):}`

`d)5x(x-2023)-x+2023=0`

`<=>(x-2023)(5x-1)=0`

`<=>[(x=2023),(x=1/5):}`

`a)2x(3x-1)+y(3x-1)=(3x-1)(2x+y)`

`b)3(x-y)-5x(x-y)=(x-y)(3-5x)`

`c)2(x+y)-2y(x+y)=2(x+y)(1-y)`

`d)y(x+1)-(x+1)(2y-1)`

`=(x+1)(y-2y+1)`

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

`e)4x^2(x-y)-(y-x)`

`=(x-y)(4x^2+1)`

`f)(x-y)^2-(y-x)(x-3y)`

`=(x-y)(x-y+x-3y)`

`=(x-y)(2x-4y)=2(x-y)(x-2y)`

`g)(x-y)^2-(y-x)(x-3y)`

`=(x-y)(x-y+x-3y)`

`=(x-y)(2x-4y)=2(x-y)(x-2y)`

`a)x^3-x`

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

`b)4x^5y^4-6x^3y^3+10x^2y^2`

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

`c)2x^2y-6xy^3`

`=2xy(x-3y^2)`

`d)5x^2y^3-25x^3y^4+10x^3y^3`

`=5x^2y^3(1-5xy+2x)`

`10)(1/4-2/5):3/8+(3/4-8/5):3/8`

`=(1/4+3/4-2/5-8/5):3/8`

`=(1-2):3/8=(-1):3/8=-8/3`

`12)(4/15+3/5):5/6+(11/15-8/5):5/6`

`=(4/15+11/15+3/5-8/5):5/6`

`=(1-1):5/6=0:5/6=0`

`14)11/15*(-19/13)+11/15*(-7/13)+4/5`

`=11/15.(-19/13-7/13)+4/5`

`=11/15.(-2)+4/5`

`=-22/15+4/5=-10/15=-2/3`

`16)5/14*12 1/2-5/14*5 1/2`

`=5/14*(12 1/2-5 1/2)`

`=5/14*7=5/2`

Chiều rộng hình chữ nhật là `1500:50=30(cm)`

mà chiều rộng `=x+5=>x=30-5=25(cm)`

`=>` chọn B

3C(hình thang cân có 2 cạnh bên bằng nhau nhưng 2 cạnh bên bằng nhau chưa chắc là hình thang cân)

4A vì B,C,D hình thoi đều có tính chất đấy rồi

`(x^3-64)/(x^3+8):(-(4-x)/(x^2-2x+4))`

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

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

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