Question

which are differences of perfect cubes? Check all that apply. 9a3 – 27 125a12 – 72 216a6 – 27y3 8a15 – 27 225a3 – 216

Answer 1

he's right its C.) and D.)

Explanation:

I just took the test on edg

Answer 2

The correct choices are:

`{8a}^(15) - 27`

and

`216 {a}^(6) - 27 {y}^(3)`

EXPLANATION

A difference of perfect cube is of the form:

`{(m)}^(3) - {(n)}^(3)`

We can rewrite

`216 {a}^(6) - 27 {y}^(3)`

Try rewriting the terms as powers to an exponent of 3.

`216 {a}^(6) - 27 {y}^(3) = {6}^(3)( {a}^(2))^(3) - {3}^(3) {y}^(3)`

This implies that:

`216 {a}^(6) - 27 {y}^(3) = ( 6 {a}^(2))^(3) - {(3y)}^(3)`

Hence this is a difference of perfect cube.

Also, we can rewrite

`{8a}^(15) - 27`

as

`{8a}^(15) - 27 = {2}^(3) ( {a}^(5))^(3) - {3}^(3)`

`{8a}^(15) - 27= {(2{a}^(5))}^(3) - {3}^(3)`