Question

what is the factored form of $x^6 - 9$?○ $(x + 3)(x - 3)$○ $(x^5 + 3)(x - 3)$○ $(x^3 + 3)(x^2 - 3)$○ $(x^3 + 3)(x^3 - 3)$done

Explanation:

Step1: Recognize difference of squares

Recall $a^2 - b^2=(a+b)(a-b)$. Rewrite $x^6 - 9$ as $(x^3)^2 - 3^2$.

Step2: Apply difference of squares formula

Substitute $a=x^3$, $b=3$ into the formula:
$(x^3)^2 - 3^2=(x^3 + 3)(x^3 - 3)$

Answer:

$\boldsymbol{(x^3 + 3)(x^3 - 3)}$