What is factor 216m^3-n^{21}p^9 ?

The solution to factor 216m^3-n^{21}p^9 is (6m-n^7p^3)(36m^2+6mn^7p^3+n^{14}p^6)

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factor 216m^3-n^{21}p^9

factor

216 m^{3} - n^{21} p^{9}

(6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})

Solution steps

216 m^{3} - n^{21} p^{9}

Rewrite

216 m^{3}

(6 m)^{3}

Rewrite

n^{21} p^{9}

(n^{7} p^{3})^{3}

= (6 m)^{3} - (n^{7} p^{3})^{3}

Apply Difference of Cubes Formula:

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

(6 m)^{3} - (n^{7} p^{3})^{3} = (6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2})

= (6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2})

Simplify

(6 m - n^{7} p^{3}) ((6 m)^{2} + 6 m n^{7} p^{3} + (n^{7} p^{3})^{2}) : (6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})

= (6 m - n^{7} p^{3}) (36 m^{2} + 6 m n^{7} p^{3} + n^{14} p^{6})

- (x cos (x))

121 + 198 \times 6 + 81 \times 12

n^{2 x} - 9

x \cdot y^{'} (x) + y x ln (y)

What is factor 216m^3-n^{21}p^9 ?
The solution to factor 216m^3-n^{21}p^9 is (6m-n^7p^3)(36m^2+6mn^7p^3+n^{14}p^6)