Question

What is the factored form of 8x24-27y6

Answer 1

Answer:

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Step-by-step 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