How to factorise a^6 -8a^3 + 27
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(a^2)^3+(-2a)^3+3^3
=(a^2-2a+3)[(a^2)^2+(-2a)^2+3^2-a^2*(-2a)-(-2a)*3-3*(a^2)]-3(a^2)(-2a)*3
=(a^2-2a+3)[a^4+4a^2+9+2a^3+6a-3a^2]+18a^3
=(a^2-2a+3)[(a^2)^2+(-2a)^2+3^2-a^2*(-2a)-(-2a)*3-3*(a^2)]-3(a^2)(-2a)*3
=(a^2-2a+3)[a^4+4a^2+9+2a^3+6a-3a^2]+18a^3
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