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In this tutorial, we are asked to simplify the expression x cubed minus 27 times x plus 3 times x square minus 3x plus 9 using the difference of cubes formula. By recognizing that x cubed minus 27 can be written as x cubed plus 3 cubed, we can apply the formula a cube plus B cube equals a plus B times a square minus a B plus B square to simplify the expression. This results in the final expression of x cubed minus 27 times x plus 3 equals x cubed minus 27 times x plus 3. By applying the sum and difference of cubes formula, we can efficiently simplify complex expressions.