Question

Which expression is a sum of cubes?

Answer 1

ANSWER

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

EXPLANATION

When we can write an expression in the form

${(x)}^{3} + {(y)}^{3}$

then it is a sum of cubes.

To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.

This tells us that the first option will be the best choice.

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

We can rewrite this as:

${ (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3}$

We apply this property of exponents:

$({a}^{m} )^{n} = {a}^{mn}$

This gives us

${( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3}$

Therefore the correct option is A

Answer 2

Answer:

-27a³b⁶+ 8a⁹b¹²

Step-by-step explanation:

In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.

The exponents of a and b in both terms in the expression are divisible by 3.

The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.