Question

Which expression is a sum of cubes?

Answer 1

Answer:

$-27 a^3 b^6 + 8 a^9 b^{12}$

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:

$-27 a^3 b^6 + 8 a^9 b^{12}$

and take cubic root to each term, we get:

$x = \sqrt[3]{-27 a^3 b^6}$

$x =\sqrt[3]{-27} \sqrt[3]{a^3} \sqrt[3]{b^6}$

$x = -3 a b^2$

$y = \sqrt[3]{8 a^9 b^{12}}$

$y =\sqrt[3]{8} \sqrt[3]{a^9} \sqrt[3]{b^{12}}$

$y =2 a^3 b^4$

The other options are not sum of cubes because 9, -9, b^10 and b^8 are not a perfect cubes.