What is factor z^3-125h^3 ?

The solution to factor z^3-125h^3 is (z-5h)(z^2+5zh+25h^2)

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factor z^3-125h^3

factor

z^{3} - 125 h^{3}

(z - 5 h) (z^{2} + 5 z h + 25 h^{2})

Solution steps

z^{3} - 125 h^{3}

Apply exponent rules

= z^{3} - (5 h)^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

z^{3} - (5 h)^{3} = (z - 5 h) (z^{2} + z \cdot 5 h + (5 h)^{2})

= (z - 5 h) (z^{2} + z \cdot 5 h + (5 h)^{2})

Simplify

z^{2} + z \cdot 5 h + (5 h)^{2} : z^{2} + 5 z h + 25 h^{2}

= (z - 5 h) (z^{2} + 5 z h + 25 h^{2})

- \frac{1}{4} (8)

- 8 - (- 14)

9 x^{2} - 15 x

(3 x^{2} - 7 x - 2) (2 x^{2} - x - 1)

(x + 9) (x - 5)

What is factor z^3-125h^3 ?
The solution to factor z^3-125h^3 is (z-5h)(z^2+5zh+25h^2)