Factor z^3+125

Problem

z3+125

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

125=5

3. Determine the terms for the formula by setting a=z and b=5

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

(z+5)*(z2−(z)*(5)+5)

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

z2−5*z+25

Final Answer

z3+125=(z+5)*(z2−5*z+25)

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