Question

What is the factored form of 8x24-27y6

Answer 1

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Explanation:

Answer 2

For this case we must factor the following expression:

`8x^(24) -27y ^ 6`

So:

We rewrite
`8x^(24)\ as\ (2x ^ 8) ^ 3`

We rewrite
`27y ^ 6\ as\ (3y ^ 2) ^ 3`

(2x ^ 8) ^ 3- (3y ^ 2) ^ 3

Since both terms are perfect cubes, factor using the cube difference formula:

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

Where:

`a = 2x ^ 8\\b = 3y ^ 2`

Rewriting:

`(2x ^ 8-3y ^ 2) ((2x ^ 8) ^ 2 + (2x ^ 8) (3y ^ 2) + (3y ^ 2) ^ 2) =\\(2x ^ 8-3y ^ 2) (4x ^(16) + 6x ^ 8y ^ 2 + 9y ^ 4)`

ANswer:

Option C