`12B`

`13A`

`1C`

`2D`

`3D`

`4D`

`5A`

`6D`

`7C`

`8B`

Chọn đáp án `A`

a, `(x^2-x+2)^2+(x-2)^2`

`=x^4-2x^3+5x^2-4x+4+x^2-4x+4`

`=x^4-2x^3+6x^2-8x+8`

`=x^4-2x^3+2x^2+4x^2-8x+8`

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

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

b, `x^4-9x^3+28x^2-36x+16`

`=x^4-4x^3-5x^3+20x^2+8x^2-32x-4x+16`

`=x^3(x-4)-5x^2(x-4)+8x(x-4)-4(x-4)`

`=(x-4)(x^3-5x^2+8x-4)`

`=(x-4)(x^3-2x^2-3x^2+6x+2x-4)`

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

`=(x-4)(x-2)(x^2-3x+2)`

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

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

c, `10x^4-27x^3y-110x^2y^2-27xy^3+10y^4`

`=10x^4+5x^3y-32x^3y-16x^2y^2-94x^2y^2-47xy^3+20xy^3+10y^4`

`=5x^3(2x+y)-16x^2y(2x+y)-47xy^2(2x+y)+10y^3(2x+y)`

`=(2x+y)(5x^3-16x^2y-47xy^2+20y^3)`

`=(2x+y)(5x^3+10x^2y-26x^2y-52xy^2+5xy^2+10y^3)`

`=(2x+y)[5x^2(x+2y)-26xy(x+2y)+5y^2(x+2y)]`

`=(2x+y)(x+2y)(5x^2-26xy+5y^2)`

`=(2x+y)(x+2y)(5x^2-25xy-xy+5y^2)`

`=(2x+y)(x+2y)[5x(x-5y)-y(x-5y)]`

`=(2x+y)(x+2y)(x-5y)(5x-y)`

d, `x^4-2y^4-x^2y^2+x^2+y^2`

`=x^4-2x^2y^2+x^2+x^2y^2-2y^4+y^2`

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

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

a, `4x(x+y)(x+z)(x+y+z) + y^2z^2`

`=4(x^2+xy+xz+yz)(x^2+zy+xz)+y^2z^2`

`=4(x^2+xy+xz)^2+4(x^2+xy+xz)yz+y^2z^2`

`=(2x^2+2xy+2xz+yz)^2`

b, `3(x^4+x^2+1)-(x+x+1)^2`

`=3x^4+3x^2+3-x^4-2x^3-3x^2-2x-1`

`=2x^4-2x^3-2x+2`

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

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

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

c, `2x^4-x^3y+3x^2y^2-xy^3+2y^4`

`=2x^4-2x^3y+2x^2y^2+x^3y-x^2y^2+xy^3+2x^2y^2-2xy^3+2y^4`

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

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

d, `bc(a+d)(b-c)+ac(b+d)(c-a)+ab(c+d)(a-b)`

`=bc(ab+bd-ac-cd)+ac(bc+cd-ab-ad)+ab(ac+ad-bc-bd)`

`=ab^2c+b^2cd-abc^2-bc^2d+abc^2+ac^2d-a^2bc-a^2cd+a^2bc+a^2bd-ab^2c-ab^2d`

`=b^2cd-bc^2d+ac^2d-a^2cd+a^2bd-ab^2d`

`=d(b^2c-bc^2+ac^2-a^2c+a^2b-ab^2)`

`=d[ab(a-b)+c^2(a-b)-(ac+bc)(a-b)]`

`=d(a-b)(ab+c^2-ac-bc)`

`=d(a-b)(b-c)(a-c)`

d, `4xy(x^2+y^2) -6(x^3+y^3+x^2y+xy^2)+9(x^2+y^2)`

`=4xy(x^2+y^2)-6[(x^3+xy^2)+(y^2+x^2y)]+9(x^2+y^2)`

`=4xy(x^2+y^2)-6[(x^2+y^2)(x+y)]+9(x^2+y^2)`

`=(x^2+y^2)(4xy-6x-6y+9)`

`=(x^2+y^2)[2x(2y-3)-3(2y-3)]`

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

Chu vi của hình vuông đó là:

`2(22+18)=80(dm)`

Một cạnh của hình vuông là:

`80:4=20(dm)=2(m)`

Diện tích của hình vuông đó là:

`2*2=4(m^2)`

a, `x^3-1+5x^2-5+3x-3`

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

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

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

`=(x-1)(x^2+6x+9)`

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

b, `x^3-3x^2+3x-1+y^3`

`=(x-1)^3+y^3`

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

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

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

c, `x^3-x^2-x+1`

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

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

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

d, `5x^3-3x^2y-45xy^2 +27y^3`

`=(5x^3-45xy^2) - (3x^2y-27y^3)`

`=5x(x^2-9y^2) - 3y(x^2-9y^2)`

`=(x^2-9y^2)(5x-3y)`

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

e, `x^4-x^2+2x-1`

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

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

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

f, `4a^2b^2 - (a^2+b^2-1)^2`

`=(a^2+b^2-1+2ab)(-a^2-b^2+1+2ab)`

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

`=(a+b+1)(a+b-1)(a-b+1)(-a+b+1)`

Gọi CTHH của hợp chất là: `S_xO_y`     `(x,y>0)`

`d_(\frac{M_(hc)}{29}=2,75862`

`=>M_(hc)=80`

`=> 32x+16y=80`

mà `32x:16y=2:3`

`=>{(x=1),(y=3):}`

`=>CTHH:SO_3`

a, Xét `\triangleADB` và `\triangleAEC` có:

`AD=AE`

`\hat{A}` chung

`AB=AC`

`=>\triangleADB=\triangleAEC(c.g.c)`     `(đpcm)`

b, Ta có: `\triangleADB=\triangleAEC`

`=>\hat{ABD}=\hat{ACE}`

mà `\hat{ABC}=\hat{ACB}`   (do `\triangleABC` cân tại `A`)

`=>\hat{IBC}=\hat{ICB}`

`=>\triangleIBC` cân tại `I`

`=> IB=IC`

Xét `\triangleABI` và `\triangleACI` có:

`AB=AC`

`\hat{ABI}=\hat{ACI}`

`BI=CI`

`=>\triangleABI=\triangleACI(c.g.c)`

`=>\hat{BAI}=\hat{CAI}`

`=>AI` là tia phân giác của `\hat{EAD}`

c, Gọi giao điểm của `AI` với `ED,BC` là `F,G`

Xét `\triangleAEF` và `\triangleADF` có:

`AE=AD`

`\hat{EAF}=\hat{DAF}`

`AF` cạnh chung

`=>\triangleAEF=\triangleADF(c.g.c)`

`=>\hat{AFE}=\hat{AFD}`

mà `\hat{AFE}+\hat{AFD}=180^o`

`=>\hat{AFE}=90^o`

`=>AF\botED` hay `AI\botED`       `(1)`

Xét `\triangleABG` và `\triangleACG` có:

`AB=AC`

`\hat{BAG}=\hat{CAG}`

`AG` cạnh chung

`=>\triangleABG=\triangleACG(c.g.c)`

`=>\hat{AGB}=\hat{AGC}`

mà `\hat{AGB}+\hat{AGC}=180^o`

`=>\hat{AGB}=90^o`

`=>AG\botBC` hay `AI\botBC`     `(2)`

Từ `(1),(2)=>ED//BC`    `(đpcm)`