Form3 Fatorization

(1) x^729 + y^729; Use identity a^3 + b^3 = (a + b)(a^2 - ab + b^2)
= (x^243 + y^243)(x^486 - x^243y^243 + y^486)
= (x^81 + y^81)(x^162 - x^81y^81 + y^162)(x^486 - x^243y^243 + y^486)
= (x^27 + y^27)(x^54 - x^27y^27 + y^54)(x^162 - x^81y^81 + y^162)(x^486 - x^243y^243 + y^486)
= (x^9 + y^9)(x^18 - x^9y^9 + y^18)(x^54 - x^27y^27 + y^54)(x^162 - x^81y^81 + y^162)(x^486 - x^243y^243 + y^486)
= (x^3 + y^3)(x^6 - x^3y^3 + y^6)(x^18 - x^9y^9 + y^18)(x^54 - x^27y^27 + y^54)(x^162 - x^81y^81 + y^162)(x^486 - x^243y^243 + y^486)
= (x + y)(x^2 - xy + y^2)(x^6 - x^3y^3 + y^6)(x^18 - x^9y^9 + y^18)(x^54 - x^27y^27 + y^54)(x^162 - x^81y^81 + y^162)(x^486 - x^243y^243 + y^486)
(2) y^4 - 25y^2 + 144
= (y^2)^2 - 25(y^2) + 144
= (y^2)^2 - 16(y^2) - 9(y^2) + 144
= (y^2)(y^2 - 16) - 9(y^2 - 16)
= (y^2 - 9)(y^2 - 16)
= (y + 3)(y - 3)(y + 4)(y - 4)

第一題唔係Form3 Fatorization,