Question

Factored form of x^12 y^16+1

Answer 1

let's recall that

1² = 1

1⁴ = 1

1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

`\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^(12)y^(18)+1\implies x^(4\cdot 3)y^(6\cdot 3)+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^(12)-x^4y^6+1)`

Answer 2

B

Explanation: