Verified answer

USE FORMULA a^3 - b^3 = ( a-b) ( a^2 + ab + b^2)

27x^3y^9 - 8z^12 = (3xy^3)^3 - ( 2z^4)^3 = ( 3xy^3- 2z^4) ( 9x^2y^6 + 6xy^3z^4 + 4z^8) ANSWER

recognise each term as a cube

ie 27x^3 y^9 = (3xy^3)^3

and 8z^12 = (2z^4)^3

we have a difference of 2 cubes

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

(3x y^3 -2z^4)(9x^2 y^6 + 6x y^3 z^4 +4 z^8)

27x^3y^9 - 8z^12

= (3xy^3 - 2z^4)(9x^2y^6 + 6xy^3z^4 + 4z^8

27x^3y^9 - 8z^12=

3^3x^3(y^3)^3-2^3(z^4)^3

use a^3-b^3 formula where (a-b)(a^2+ab+b^2)

So you get

(3xy^3-2z^4)(9x^2y^6+6xy^3z^4+4z^8)

27 is 3^3 and 8 is 2^3

therefore we have the a^3-b^3 form (cz every exposant can be divided by 3) where a is 3xy^3 and b is 2z^4

the formula says that

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

therefore we have

(3xy^3-2z^4)(9x^2y^6+6xy^3z^4+4z^8)