Factor z^3+64

Problem

z^3+64

Solution

1. Identify the expression as a sum of two cubes, which follows the form a^3+b^3

2. Rewrite the constant 64 as a cube, which is 4^3

3. Apply the formula for the sum of cubes: a^3+b^3=(a+b)*(a^2−a*b+b^2)

4. Substitute a=z and b=4 into the formula.

5. Simplify the terms within the resulting quadratic factor.

Final Answer

z^3+64=(z+4)*(z^2−4*z+16)

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