What is factor m^9n^{15}+p^3 ?

The solution to factor m^9n^{15}+p^3 is (m^3n^5+p)(m^6n^{10}-m^3n^5p+p^2)

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factor m^9n^{15}+p^3

factor

m^{9} n^{15} + p^{3}

(m^{3} n^{5} + p) (m^{6} n^{10} - m^{3} n^{5} p + p^{2})

Solution steps

m^{9} n^{15} + p^{3}

Rewrite

m^{9} n^{15}

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

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(m^{3} n^{5} + p) ((m^{3} n^{5})^{2} - p m^{3} n^{5} + p^{2}) : (m^{3} n^{5} + p) (m^{6} n^{10} - m^{3} n^{5} p + p^{2})

= (m^{3} n^{5} + p) (m^{6} n^{10} - m^{3} n^{5} p + p^{2})

e^{2 t} u (- t)

am + 2 bm - 3 c m + 12 c n - 4 an - 8 bn

4 (x - y)^{2} - 12 (x - y) + 9

8 m^{3} + 4 m^{2} - n^{3} - n^{2}

a x + 2 b x + 4 b y + 2 a y

What is factor m^9n^{15}+p^3 ?
The solution to factor m^9n^{15}+p^3 is (m^3n^5+p)(m^6n^{10}-m^3n^5p+p^2)