What is the factored form of x 12y 18 1


Asked by maham237 @ in Mathematics viewed by 292 People


x^12y^18+1

Answered by maham237 @



Answer: The required factored form of the given expression is

(x^4y^6+1)(x^8y^{12}-x^4y^6+1).

Step-by-step explanation: We are given to find the factored form of the following algebraic expression:

E=x^{12}y^{18}+1.

We will be using the following formula:

a^3+b^3=(a+b)(a^2+ab+b^2).

Now, we have

E\\\\=x^{12}y^{18}+1\\\\=(x^4y^6)^3+1^3\\\\=(x^4y^6+1)\{(x^4y^6)^2-x^4y^6\times1+1^2\}\\\\=(x^4y^6+1)(x^8y^{12}-x^4y^6+1).

Thus, the required factored form of the given expression is

(x^4y^6+1)(x^8y^{12}-x^4y^6+1).


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