Verified answer

To assist you visually, Dr. Pan (MathDoc) has recorded a YouTube video. Since this is a typical exam question, the video also addresses several pitfalls you want to avoid in solving this type of problem.

Please leave a comment on YouTube and let her know if it helped you. Thanks!

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Just visualize it as:

(x^2)^3 + (1^2)^3

Remember:

"A power term raised to a power" means you multiply the exponents to make one master exponent.

Now you see:

A = x^2

B = 1^2

Thus you have

A^3 + B^3

And factored, it is:

(A + B)*(A^2 - A*B + B^2)

And plug in A and B:

((x^2) + (1^2))*((x^2)^2 - (x^2)*(1^2) + (1^2)^2)

Simplify:

(x^2 + 1)*(x^4 - x^2 + 1)

You have the right formula, but it factors into...

(x^3+1)(X^6-X^3+1), you can also check that by multiplying the factors together.

just pretend the ^9 isnt there. Lemme give you an example:

x^9 + 27 = x^3 , 3

(x^3 + 3)(x^6 - 3x^3 + 9)

I'm pretty sure that's right.

manipulate the equation

(x^3) ^3 + 1^3

so...

(x^3)^3 + 1^3 = (x^3 + 1)(X^6 - x^3 + 1)