Factorization

a^4+b^4 cannot be factorized.
a^6-b^6
=(a^2)^3-(b^2)^3
=(a^2-b^2)(a^4+a^2*b^2+b^4)
=(a+b)(a-b)(a^4+2a^2*b^2-a^2*b^2+b^4)
=(a+b)(a-b)[(a^2+b^2)^2-(ab)^2]
=(a+b)(a-b)(a^2+ab+b^2)(a^2-ab+b^2)
a^10-b^10
=(a^5)^2-(b^5)^2
=(a^5+b^5)(a^5-b^5)
=(a+b)(a^4-a^3*b+a^2*b^2-a*b^3+b^4)(a-b)(a^4+a^3*b+a^2*b^2+a*b^3+b^4)

a^4-b^4 = (a^2) ^ 2 - (b^2) ^ 2 = (a^2-b^2)(a^2+b^2) = (a-b)(a+b)(a^2+b^2)

a^6-b^6 = (a^2) ^ 3 - (b^2) ^ 3 = (a^2 - b^2) * (a^4 + a^2b^2 + b^4) = (a-b)(a+b)(a^4 + a^2b^2 + b^4)

a^10-b^10 = (a^5) ^ 2 - (b^5) ^ 2 = (a^5-b^5)(a^5+b^5)

因為係加既關係，a^4+b^4係唔可以Factorize架喎，點解會咁問？

a^6 - b^6
= (a^3 + b^3) (a^3 - b^3)
= (a+b) (a^2 - ab + b^2) (a-b) (a^2 +ab + b^2)

a^10-b^10
= (a^5 + b^5) (a^5 - b^5)