Answer: (x³ + 3)(x³ - 3)
Explanation: A variable taken to any even power is a perfect square. Its factors will have exponents equal to one-half the original power.
In this case, x⁶ would therefore be a perfect square.
Since 9 is also a perfect square,
what we have here is the difference of two squares.
That can be factored as the product of two binomials,
one with a plus and one with a minus.
So we have ( + )( - ).
Now ask yourself "what are the factors of x⁶ that are the same?"
Remember the rule is that those factors will use
one-half the exponent on the original.
So the factors of x⁶ that are the same are x³ and x³.
The factors of 9 that are the same are 3 and 3.
So our answer is (x³ + 3)(x³ - 3) and that's all there is to it.
