What is factor 125n^9p^6-27s^6f^3 ?

The solution to factor 125n^9p^6-27s^6f^3 is (5n^3p^2-3s^2f)(25n^6p^4+15n^3p^2s^2f+9s^4f^2)

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factor 125n^9p^6-27s^6f^3

factor

125 n^{9} p^{6} - 27 s^{6} f^{3}

(5 n^{3} p^{2} - 3 s^{2} f) (25 n^{6} p^{4} + 15 n^{3} p^{2} s^{2} f + 9 s^{4} f^{2})

Solution steps

125 n^{9} p^{6} - 27 s^{6} f^{3}

Rewrite

125 n^{9} p^{6}

(5 n^{3} p^{2})^{3}

Rewrite

27 s^{6} f^{3}

(3 s^{2} f)^{3}

= (5 n^{3} p^{2})^{3} - (3 s^{2} f)^{3}

Apply Difference of Cubes Formula:

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

(5 n^{3} p^{2})^{3} - (3 s^{2} f)^{3} = (5 n^{3} p^{2} - 3 s^{2} f) ((5 n^{3} p^{2})^{2} + 5 n^{3} p^{2} 3 s^{2} f + (3 s^{2} f)^{2})

= (5 n^{3} p^{2} - 3 s^{2} f) ((5 n^{3} p^{2})^{2} + 5 n^{3} p^{2} 3 s^{2} f + (3 s^{2} f)^{2})

Simplify

(5 n^{3} p^{2} - 3 s^{2} f) ((5 n^{3} p^{2})^{2} + 5 n^{3} p^{2} \cdot 3 s^{2} f + (3 s^{2} f)^{2}) : (5 n^{3} p^{2} - 3 s^{2} f) (25 n^{6} p^{4} + 15 n^{3} p^{2} s^{2} f + 9 s^{4} f^{2})

= (5 n^{3} p^{2} - 3 s^{2} f) (25 n^{6} p^{4} + 15 n^{3} p^{2} s^{2} f + 9 s^{4} f^{2})

(\frac{3 π}{2}) + 2 π

sin^{(2)} (x) + 6 x - 2

[X + 4]

3 x^{2} + (2 x - 5)

\frac{e ^{3} - 1}{3 e}

What is factor 125n^9p^6-27s^6f^3 ?
The solution to factor 125n^9p^6-27s^6f^3 is (5n^3p^2-3s^2f)(25n^6p^4+15n^3p^2s^2f+9s^4f^2)