What is factor 8n^3-27m^3 ?

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

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factor 8n^3-27m^3

factor

8 n^{3} - 27 m^{3}

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

Solution steps

8 n^{3} - 27 m^{3}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

\frac{1}{2 \cdot 2 ^{n - 1} \cdot { 2 ( 2 ^{n} - 1 ) + ( 2 ^{n - 1} - 1 ) \cdot 2 }}

\frac{- 21 y ^{3}}{- 3 y ^{2}}

(m^{c})^{1}

(x^{2} + 4 x + 3) (2 x^{2} - 9 x + 7)

\frac{1}{cos ^{2} ( x )} + \frac{1}{sin ^{2} ( x )}

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