Factor 27-x^3

Problem

27−x3

Solution

1. Identify the expression as a difference of two cubes.

2. Rewrite the terms as perfect cubes to identify the bases.

27=3

x3=(x)3

3. Apply the formula for the difference of cubes, which is a3−b3=(a−b)*(a2+a*b+b2)

4. Substitute a=3 and b=x into the formula.

(3−x)*(3+3*x+x2)

5. Simplify the terms inside the second set of parentheses.

3=9

Final Answer

27−x3=(3−x)*(9+3*x+x2)

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