Question

What is the factored form of x12y18+1

Answer 1

For this case we must factor the following expression:

$x^{12}y{18}+1$

We rewrite $x^{12}y^{18}$as $(x ^ 4y ^ 6) ^ 3:$

$(x ^ 4y ^ 6) ^ 3 + 1$

Being both perfect cube terms, it is factored by applying the cube sum formula:

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

Where:

$a = x ^ 4y ^ 6\\b = 1$

So:

$(x ^ 4y ^ 6 + 1) ((x ^ 4y ^ 6) ^ 2-x ^ 4y ^ 6 + 1 ^ 2) =\\(x ^ 4y ^ 6 + 1) (x ^ {8} y ^ {12} -x ^ 4y ^ 6 + 1)$

Answer:

Option B

Answer 2

the answer is........ B