(3a-1)^3-27=(3a-1)^3-3^3=? (3b+2)^3-64=(3b+2)^3-4^3=? (x-3)^3+(x+3)^3=?

Question

(3a-1)^3-27=(3a-1)^3-3^3=?

(3b+2)^3-64=(3b+2)^3-4^3=?

(x-3)^3+(x+3)^3=?

Answer 1

(3a-1)^3-3^3=(3a-1-3)((3a-1)^2+3(3a-1)+3^2)=(3a-4)(9a^2-6a+1+9a-3+9)=(3a-4)(9a^2+3a+6)

(3b+2)^3-4^3=(3b+2-4)((3b+2)^2+4(3b+2)+4^2)=(3b-2)(9b^2+6b+4+12b+8+16)=(3b-2)*

(9b^2+18b+28)

(x-3)^3+(x+3)^3=(x-3+x+3)((x-3)^2-(x-3)(x+3)+(x+3)^2)=x(x^2-6x+9-x^2+9+x^2+6x+9)=x*(18+x^2)