What is factor d^3e^6f^9-216 ?

The solution to factor d^3e^6f^9-216 is (e^2df^3-6)(e^4d^2f^6+6e^2df^3+36)

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factor d^3e^6f^9-216

factor

d^{3} e^{6} f^{9} - 216

(e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)

Solution steps

d^{3} e^{6} f^{9} - 216

Rewrite

d^{3} e^{6} f^{9}

(d e^{2} f^{3})^{3}

= (d e^{2} f^{3})^{3} - 216

Rewrite

216

6^{3}

= (d e^{2} f^{3})^{3} - 6^{3}

Apply Difference of Cubes Formula:

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

(d e^{2} f^{3})^{3} - 6^{3} = (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 6^{2})

= (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 6^{2})

Refine

= (d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 36)

Simplify

(d e^{2} f^{3} - 6) ((d e^{2} f^{3})^{2} + 6 d e^{2} f^{3} + 36) : (e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)

= (e^{2} d f^{3} - 6) (e^{4} d^{2} f^{6} + 6 e^{2} d f^{3} + 36)

+ a^{2} - x y + a x - a y

4 e^{2} + 7 e^{3} + 9 e^{4}

\frac{x ^{2} - 3 x}{x}

3^{(n + 3)} - 27

4 a x + b + b x + 4 a

What is factor d^3e^6f^9-216 ?
The solution to factor d^3e^6f^9-216 is (e^2df^3-6)(e^4d^2f^6+6e^2df^3+36)