Question

What is the factored form of x^12y^18+1?

Answer 1

the answer to that is (x^4 y^6+1)(x^8 y^12-x^4 y^6+1

Answer 2

`(x^4y^6+1)(x^8y^(12)-x^4y^6+1)`

Explanation:

We have been given an expression
`x^(12)y^(18)+1` and we are asked to factor our given expression.

We will use sum of cubes formula to factor our given expression.

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

Upon using power rule of exponents
`a^(bc)=(a^b)^(c)`, we can write:

`x^(12)=(x^4)^3`

`y^(18)=(y^6)^3`

We can write 1 as
`1^3` as 1 raised to any power equals 1.

Now we are ready to apply sum of cubes formula.

`(x^4y^6)^3+1^3=(x^4y^6+1)((x^4y^6)^2-x^4y^6+1^2)`

Upon simplifying right side of our equation we will get,

`(x^4y^6)^3+1=(x^4y^6+1)(x^(4*2)y^(6*2)-x^4y^6+1)`

`(x^4y^6)^3+1=(x^4y^6+1)(x^8y^(12)-x^4y^6+1)`

Therefore, after factoring our given expression we get
`(x^4y^6+1)(x^8y^(12)-x^4y^6+1)`.