Factor x^3+27

Problem

x3+27

Solution

1. Identify the expression as a sum of two cubes, since x3 is a cube and 27=3

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

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

4. Simplify the terms within the second factor by calculating 3=9 and x⋅3=3*x

Final Answer

x3+27=(x+3)*(x2−3*x+9)

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