Answer:
[tex]-27 a^3 b^6 + 8 a^9 b^{12} [/tex]
Step-by-step explanation:
In the picture attached, the problem is shown.
A polynomial in the form x³ + y³ is called a sum of cubes
If we take the expression:
[tex]-27 a^3 b^6 + 8 a^9 b^{12} [/tex]
and take cubic root to each term, we get:
[tex] x = \sqrt[3]{-27 a^3 b^6} [/tex]
[tex] x =\sqrt[3]{-27} \sqrt[3]{a^3} \sqrt[3]{b^6}[/tex]
[tex] x = -3 a b^2[/tex]
[tex]y = \sqrt[3]{8 a^9 b^{12}} [/tex]
[tex] y =\sqrt[3]{8} \sqrt[3]{a^9} \sqrt[3]{b^{12}}[/tex]
[tex] y =2 a^3 b^4[/tex]
The other options are not sum of cubes because 9, -9, b^10 and b^8 are not a perfect cubes.
