Question

What is the factored form of x ^ 9 + 27 ?

Answer 1

The general form of factorizing the sum of two perfect cubes is:

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

Factor the given expression:

`\begin{gathered} x^9+27 \\ x^9+27=(x^3)^3+3^3 \\ \text{put } \\ a=x^3,b=3\text{ into the cubic formula} \\ a^2=(x^3)^2=x^6 \\ ab=3x^3 \\ b^2=3^2=9 \\ \end{gathered}`

Therefore,

`a^3+b^3=(a+b)(a^2-ab+b^2)=(x^3+3)(x^6-3x^3+9)`

The correct answer is option B