Question

What is the factored form of x12y18+1

Answer 1

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

Answer 2

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