Respuesta :
Answer:
[tex](x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]
Step-by-step explanation:
We have been given an expression [tex]x^{12}y^{18}+1[/tex] and we are asked to factor our given expression.
We will use sum of cubes formula to factor our given expression.
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
Upon using power rule of exponents [tex]a^{bc}=(a^b)^{c}[/tex], we can write:
[tex]x^{12}=(x^4)^3[/tex]
[tex]y^{18}=(y^6)^3[/tex]
We can write 1 as [tex]1^3[/tex] as 1 raised to any power equals 1.
Now we are ready to apply sum of cubes formula.
[tex](x^4y^6)^3+1^3=(x^4y^6+1)((x^4y^6)^2-x^4y^6+1^2)[/tex]
Upon simplifying right side of our equation we will get,
[tex](x^4y^6)^3+1=(x^4y^6+1)(x^{4*2}y^{6*2}-x^4y^6+1)[/tex]
[tex](x^4y^6)^3+1=(x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]
Therefore, after factoring our given expression we get [tex](x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex].
