Question

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

Answer 1

factors of
`x^(12)y^(18)+1 = (x^4y^6+1) (x^8y^(12) -x^4y^6 +1)`

Explanation:

We need to find factors of
`x^(12)y^(18)+1 can\,\,be\,\, written\,\, as\,\,\\(x^2y^3)^6 + 1\\It\,\, can\,\, be\,\, further\,\, written\,\, as\\((x^2y^3)^2)^3 +1\\Using\,\, the\,\, formula\,\, a^3+b^3 = (a+b)(a^2-ab+b^2)\\Here \,\, a = (x^2y^3)^2 and y = 1\\((x^2y^3)^2)^3 +(1)^3= ((x^2y^3)^2+1) (((x^2y^3)^2)^2 -(x^2y^3)^2 +1)\\= (x^4y^6+1) (x^8y^(12) -x^4y^6 +1)`

So, factors of
`x^(12)y^(18)+1 = (x^4y^6+1) (x^8y^(12) -x^4y^6 +1)`