Phân tích các đa thức sau thành nhân tử x^2+6x+9 10x-25-x^2 8x^3-1/8 1/25x^2-6y^2 x^3-1/27 (a+b)^3-(a-b)^3 (a+b)^3+(a-b)^3 8x^3+12x^2y+6xy^2+y^3 -x^3+

Đáp án:

`x^2+6x+9=x^2+2.x.3+9=(x+3)^2`

`10x-25-x^2=-(x^2-10x+25)=-(x-5)^2`

`8x^3-1/8=(2x)^3-(1/2)^3=(2x-1/2)(4x^2+x+1/4)`

`1/25x^2-6y^2=(1/5x-sqrt6y)(1/5x+sqrt6y)`

`x^3-1/27=(x)^3-(1/3)^3=(x-1/3)(x^2+1/3x+1/9)`

`(a+b)^3-(a-b)^3=(a+b-a+b)[(a+b)^2+(a-b)(a+b)+(a-b)^2]=2b(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)=2b(3a^2+b^2)`

`(a+b)^3+(a-b)^3=(a+b+a-b)[(a+b)^2-(a-b)(a+b)+(a-b)^2]=2a(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)=2a(3b^2+a^2)`

`8x^3+12x^2y+6xy^2+y^3=(2x)^3+3.(2x)^2y+3.2x(y)^2+y^3=(2x+y)^3`

`-x^3+9x^2-27x+27=-x^3+3x^2*3-3x.9+3^3=(3-x)^3`.