(1) x3+6x2y+12xy2+8y3=(x+2y)3x^3 + 6x^2y + 12xy^2 + 8y^3 = (x + 2y)^3x3+6x2y+12xy2+8y3=(x+2y)3 (2) 8x3−12x2+6x−1=(2x−1)38x^3 - 12x^2 + 6x - 1 = (2x - 1)^38x3−12x2+6x−1=(2x−1)3 (3) x3−9x2y+27xy2−27y3=(x−3y)3x^3 - 9x^2y + 27xy^2 - 27y^3 = (x - 3y)^3x3−9x2y+27xy2−27y3=(x−3y)3 (4) a3+27=(a+3)(a2−3a+9)a^3 + 27 = (a + 3)(a^2 - 3a + 9)a3+27=(a+3)(a2−3a+9) (5) 27p3−8q3=(3p−2q)(9p2+6pq+4q2)27p^3 - 8q^3 = (3p - 2q)(9p^2 + 6pq + 4q^2)27p3−8q3=(3p−2q)(9p2+6pq+4q2) (6) x6−64y6=(x3−8y3)(x3+8y3)=(x−2y)(x2+2xy+4y2)(x+2y)(x2−2xy+4y2)x^6 - 64y^6 = (x^3 - 8y^3)(x^3 + 8y^3) = (x - 2y)(x^2 + 2xy + 4y^2)(x + 2y)(x^2 - 2xy + 4y^2)x6−64y6=(x3−8y3)(x3+8y3)=(x−2y)(x2+2xy+4y2)(x+2y)(x2−2xy+4y2)