Factor z^3+27

Problem

z3+27

Solution

1. Identify the expression as a sum of two cubes, which follows the form a3+b3

2. Rewrite the constant term as a cube to find the values of a and b

27=3

3. Determine the variables for the formula by setting a=z and b=3

4. Apply the formula for the sum of cubes: a3+b3=(a+b)*(a2−a*b+b2)

5. Substitute the values into the formula.

(z+3)*(z2−(z)*(3)+3)

6. Simplify the terms inside the second factor.

(z+3)*(z2−3*z+9)

Final Answer

z3+27=(z+3)*(z2−3*z+9)

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