Rewrite as .

Rewrite as .

Since both terms are perfect cubes, factor using the sum of cubes formula, where and .

Apply the product rule to .

Raise to the power of .

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by .

Multiply by .

Multiply by .

One to any power is one.

Factor.

Rewrite in a factored form.

Rewrite the middle term.

Rearrange terms.

Factor first three terms by perfect square rule.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

Reorder terms.

Multiply by .

Reorder terms.

Remove unnecessary parentheses.

Factor 27x^6+1