What is factor 5832m^{15}n^{24}+p^{21} ?

The solution to factor 5832m^{15}n^{24}+p^{21} is (18m^5n^8+p^7)(324m^{10}n^{16}-18m^5n^8p^7+p^{14})

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factor 5832m^{15}n^{24}+p^{21}

factor

5832 m^{15} n^{24} + p^{21}

(18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

Solution steps

5832 m^{15} n^{24} + p^{21}

Rewrite

5832 m^{15} n^{24}

(18 m^{5} n^{8})^{3}

= (18 m^{5} n^{8})^{3} + p^{21}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

p^{21} = (p^{7})^{3}

= (18 m^{5} n^{8})^{3} + (p^{7})^{3}

Apply Sum of Cubes Formula:

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

(18 m^{5} n^{8})^{3} + (p^{7})^{3} = (18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} 18 m^{5} n^{8} + p^{14})

= (p^{7} + 18 m^{5} n^{8}) (p^{14} - p^{7} 18 m^{5} n^{8} + (18 m^{5} n^{8})^{2})

Simplify

(18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} \cdot 18 m^{5} n^{8} + p^{14}) : (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

= (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

2 \times 2

3 x^{2} - 2 x^{2} + 27 x - 18

(x - 2)^{2} + 6

a^{3} - 2 (a)^{2} + 20

FE (C L O^{3}) 2 + H^{2} O

What is factor 5832m^{15}n^{24}+p^{21} ?
The solution to factor 5832m^{15}n^{24}+p^{21} is (18m^5n^8+p^7)(324m^{10}n^{16}-18m^5n^8p^7+p^{14})