What is factor 8+27n^3 ?

The solution to factor 8+27n^3 is (3n+2)(9n^2-6n+4)

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factor 8+27n^3

factor

8 + 27 n^{3}

(3 n + 2) (9 n^{2} - 6 n + 4)

Solution steps

8 + 27 n^{3}

Write in the standard form

= 27 n^{3} + 8

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

(3 n)^{3} + 2^{3} = (3 n + 2) (3^{2} n^{2} - 2 \cdot 3 n + 2^{2})

= (3 n + 2) (3^{2} n^{2} - 2 \cdot 3 n + 2^{2})

Simplify

(3 n + 2) (3^{2} n^{2} - 2 \cdot 3 n + 2^{2}) : (3 n + 2) (9 n^{2} - 6 n + 4)

= (3 n + 2) (9 n^{2} - 6 n + 4)

12 \cdot 5

(- 4 a + b) (4 a + b)

(2 \cdot 3 - i) (\frac{3}{5} - 2 i)

\frac{82}{100}