What is factor m^3n^6+d^3 ?

The solution to factor m^3n^6+d^3 is (mn^2+d)(m^2n^4-mn^2d+d^2)

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factor m^3n^6+d^3

factor

m^{3} n^{6} + d^{3}

(m n^{2} + d) (m^{2} n^{4} - m n^{2} d + d^{2})

Solution steps

m^{3} n^{6} + d^{3}

Rewrite

m^{3} n^{6}

(m n^{2})^{3}

= (m n^{2})^{3} + d^{3}

Apply Sum of Cubes Formula:

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

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

= (d + m n^{2}) (d^{2} - d m n^{2} + (m n^{2})^{2})

Simplify

(m n^{2} + d) ((m n^{2})^{2} - d m n^{2} + d^{2}) : (m n^{2} + d) (m^{2} n^{4} - m n^{2} d + d^{2})

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

4 y^{2} + 12 - 7

y^{2} - 14 + 49

\frac{23}{- 140}

x + 3 - x + 3

9 x^{2} + 9

What is factor m^3n^6+d^3 ?
The solution to factor m^3n^6+d^3 is (mn^2+d)(m^2n^4-mn^2d+d^2)