What is factor m^3-216n^{12}p^3 ?

The solution to factor m^3-216n^{12}p^3 is (m-6n^4p)(m^2+6mn^4p+36n^8p^2)

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factor m^3-216n^{12}p^3

factor

m^{3} - 216 n^{12} p^{3}

(m - 6 n^{4} p) (m^{2} + 6 m n^{4} p + 36 n^{8} p^{2})

Solution steps

m^{3} - 216 n^{12} p^{3}

Rewrite

216 n^{12} p^{3}

(6 n^{4} p)^{3}

= m^{3} - (6 n^{4} p)^{3}

Apply Difference of Cubes Formula:

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

m^{3} - (6 n^{4} p)^{3} = (m - 6 n^{4} p) (m^{2} + 6 n^{4} p m + (6 n^{4} p)^{2})

= (m - 6 n^{4} p) ((6 n^{4} p)^{2} + 6 n^{4} p m + m^{2})

Simplify

(m - 6 n^{4} p) (m^{2} + 6 n^{4} p m + (6 n^{4} p)^{2}) : (m - 6 n^{4} p) (m^{2} + 6 m n^{4} p + 36 n^{8} p^{2})

= (m - 6 n^{4} p) (m^{2} + 6 m n^{4} p + 36 n^{8} p^{2})

(x - 1)^{4} - 3 x (x - 2) - 1

π - (\frac{4 π}{5})

x - 7 x + \frac{49}{4}

[x + 3 y]

7 x^{2} + 78 - 7

What is factor m^3-216n^{12}p^3 ?
The solution to factor m^3-216n^{12}p^3 is (m-6n^4p)(m^2+6mn^4p+36n^8p^2)