What is factor 8(m+3n)^3-1000(x-4)^3 ?

The solution to factor 8(m+3n)^3-1000(x-4)^3 is 8(m^3+9m^2n+27mn^2+27n^3-125x^3+1500x^2-6000x+8000)

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factor 8(m+3n)^3-1000(x-4)^3

factor

8 (m + 3 n)^{3} - 1000 (x - 4)^{3}

8 (m^{3} + 9 m^{2} n + 27 m n^{2} + 27 n^{3} - 125 x^{3} + 1500 x^{2} - 6000 x + 8000)

Solution steps

8 (m + 3 n)^{3} - 1000 (x - 4)^{3}

Factor out common term

8 : 8 ((m + 3 n)^{3} - 125 (x - 4)^{3})

= 8 ((m + 3 n)^{3} - 125 (x - 4)^{3})

Expand

(m + 3 n)^{3} - 125 (x - 4)^{3} : m^{3} + 9 m^{2} n + 27 m n^{2} + 27 n^{3} - 125 x^{3} + 1500 x^{2} - 6000 x + 8000

= 8 (m^{3} + 9 m^{2} n + 27 m n^{2} + 27 n^{3} - 125 x^{3} + 1500 x^{2} - 6000 x + 8000)

x^{6} - 81 x^{2}

\frac{( - 5 m ^{5} n ^{2} - \frac{1}{2} m ^{4} n ^{4} + \frac{2}{3} m ^{3} n - 4 m n ^{4} )}{( - 4 m ^{5} n ^{3} )}

6 - 2 (x + 5) < - 12

\frac{x + 2}{2} > 3

\frac{2}{3} x - \frac{5}{9} x = 2

What is factor 8(m+3n)^3-1000(x-4)^3 ?
The solution to factor 8(m+3n)^3-1000(x-4)^3 is 8(m^3+9m^2n+27mn^2+27n^3-125x^3+1500x^2-6000x+8000)