1/27 + a^3
= (1/3)^3 + a^3
= (1/3 + a)(1/9 + 1/3.a + a^2)
1/8x^3 + 8y^3
= (1/2x)^3 + (2y)^3
= (1/2x + 2y)( 1/4x - xy + 4y^2)
1/8x^3 - 8
= (1/2x)^3 - 2^3
= (1/2 - 2)(1/4x + 1 + 4)
(a+b)^3 - c^3
= (a+b-c)(a^2+2ab+b^2+ac+bc+c^2)
125 - (x+2)^3
= 5^3 - (x+2)^3
= (5-x+2)(25 + 5x + 10 + x^2 + 4)

1) 25x^2 - 10xy + y^2= (5x-y)^2
2 ) x^4 - 4x^2y+ 4y^2
​=x^4 - 2x^2y-2x^2y+4y^2
=(x^4 - 2x^2y)-(2x^2y-4y^2)
=x^2(x^2-2y) -2y(x^2-2y)
=(x^2-2y)((x^2-2y)
=(x^2-2y)^2
3) 9x^2 - 30x + 25 =(3x-5)^2
4) 9x^4 - 12x^2y + 4y^2 =(3x^2-2y)^2

(x-5)^3 - 27
= (x-5)^3 - 3^3
= (x-5-3)(x^2 + 10x+5 + 3x - 15 + 9)
(x+4)^3 - 64
= (x+4)^3 - 8^3
= (x+4-8)(x^2 + 8x + 16 + 8x + 32 + 64)
x^6 - 1
= (x^2)^3 - 1^3
= (x^2 - 1)(x^4 + x^2 + 1)
x^12 - y^4 
= (x^6)^2 - (y^2)^2
= (x^6 - y^2 ) (x^6 + y^2 )
x^3 + 3x^2 + 3x +1
= 3x(x+1) +x^3 + 1^3
= 3x(x+1) +(x+1)(x^2 + x+1)
= (x+1) (3x+(x^2+x+1))

x^3 + 9x^2 + 27x + 27
= (x+3)^3
x^3 + 15x^2 + 75x + 125
= (x+5)^3
m^3 - 6m^2+ 12m -8
= (m-2)^3
64 - 48m + 12m^2 - m^3
= (4-m)^3
8a^3 + 12a^2 + 6a + 1
= (2a + 1)^3

27a^3 - 27a^2 + 9a -1
= (3a - 1)^3
27a^3 - 54ba^2 + 36ab^2 - 8b^2
= (3a-2b)^2
x^4 - 4x^2y + 4y^2
= (x^2 - 2y)^2
9x^4 - 12x^2y + 4y^2
= (3x^2 - 2y)^2

9x^4 - 12x^5 + 4x^6
= (3x^2 - 2x^3)^2
9x^6 - 12x^7 +4x^8
= (3x^3 - 2x^4)^2
x^3 + 8
= x^3 + 2^3
= (x+2)(x^2 +2x +4)
8x^3 + 27y^3
= (2x)^3 + (3y)^3
= (2x+3y)(4x^2 + 6xy + 9y^2)

Hai câu này mình làm nhầm, sửa lại nhé:
x^3 + 8
= x^3 + 2^3
= (x+2)(x^2 -2x +4)
8x^3 + 27y^3
= (2x)^3 + (3y)^3
= (2x+3y)(4x^2 -6xy + 9y^2)

8x^6 - 27y^3
= (2x^2)^3 - (3y)^3
= (2x^2 - 3y)( 4x^4 + 6x^2y+ 9y^2)
1/64x^6 - 125y^3
= (1/4x^2)^3 - (5y)^3
= (1/4x^2 - 5y)(1/16x^4 + 5/4x^2y + 25y^2)
x^3 - (y-1)^3
= (x-y+1)(x^2+xy -x +y^2 - 2y +1)
(x+3)^3 -8
= (x+3)^3 + 2^3
= (x+3+2)(x^2 + 6x + 9- 2x+6 +4)
(x+1)^3 - 125
= (x+1)^3 - 5^3
= (x+1-5)(x^2 +2x+1+5x+1 + 25)

x^6 + 1
= (x^2)^3 + 1^3
= (x^2 + 1)(x^4 + x^2 + 1)
x^6 - y^6
= (x^3)^2 - (y^3)^2
= (x^3 - y^3)(x^3 +y^3)
= (x-y)(x^3 +xy+y^3)(x+y)(x^3-xy+y^3)
x^9+1
= (x^3)^3 +1^3
= (x^3 +1)(x^6- x^3 +1)
x^3 +6x^2 +12x +8
= (x+8)^3

27a^3 - 27a^2 + 9a -1
= (3a - 1)^3
27a^3 - 54ba^2 + 36ab^2 - 8b^3
= (3a-2b)^3
x^4 - 4x^2y + 4y^2
= (x^2 - 2y)^2
9x^4 - 12x^2y + 4y^2
= (3x^2 - 2y)^2

x^3+12x^2 +48x+64
= (x+4)^3
m^3 -3m^2 +3m-1
= (m-1)^3
27-27m+9m^2 -m^3
=(3-m)^3
125-75m+9m^3 -m^3
= (5-m)^3
8a^3- 12a^2 + 6a-1
= (2a-1)^3
27a^3-27a^2+9a-1
= (3a-1)^3

Rất hay .tốt