What is 27(m+2n)^3-(m-6n)^3 ?

The solution to 27(m+2n)^3-(m-6n)^3 is 26m^3+180m^2n+216mn^2+432n^3

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simplify 27(m+2n)^3-(m-6n)^3

simplify

27 (m + 2 n)^{3} - (m - 6 n)^{3}

26 m^{3} + 180 m^{2} n + 216 m n^{2} + 432 n^{3}

Solution steps

27 (m + 2 n)^{3} - (m - 6 n)^{3}

Expand

27 (m + 2 n)^{3} : 27 m^{3} + 162 m^{2} n + 324 m n^{2} + 216 n^{3}

= 27 m^{3} + 162 m^{2} n + 324 m n^{2} + 216 n^{3} - (m - 6 n)^{3}

Expand

- (m - 6 n)^{3} : - m^{3} + 18 m^{2} n - 108 m n^{2} + 216 n^{3}

= 27 m^{3} + 162 m^{2} n + 324 m n^{2} + 216 n^{3} - m^{3} + 18 m^{2} n - 108 m n^{2} + 216 n^{3}

Group like terms

= 27 m^{3} - m^{3} + 162 m^{2} n + 18 m^{2} n + 324 m n^{2} - 108 m n^{2} + 216 n^{3} + 216 n^{3}

Add similar elements:

27 m^{3} - m^{3} = 26 m^{3}

= 26 m^{3} + 162 m^{2} n + 18 m^{2} n + 324 m n^{2} - 108 m n^{2} + 216 n^{3} + 216 n^{3}

Add similar elements:

162 m^{2} n + 18 m^{2} n = 180 m^{2} n

= 26 m^{3} + 180 m^{2} n + 324 m n^{2} - 108 m n^{2} + 216 n^{3} + 216 n^{3}

Add similar elements:

324 m n^{2} - 108 m n^{2} = 216 m n^{2}

= 26 m^{3} + 180 m^{2} n + 216 m n^{2} + 216 n^{3} + 216 n^{3}

Add similar elements:

216 n^{3} + 216 n^{3} = 432 n^{3}

= 26 m^{3} + 180 m^{2} n + 216 m n^{2} + 432 n^{3}

(a - 5 b)^{2} - 16 b^{2}

2 x^{3} + 54 y^{3} - 4 x - 12 y

((2^{k})^{+})^{1} + ((2^{k})^{+})^{1} - 2

(- 3 x^{3} \cdot y^{2} \cdot z) \cdot (\frac{- 1}{3 \cdot x \cdot y ^{2}})^{3}

\frac{( 7 + x + 4.75 )}{3}

What is 27(m+2n)^3-(m-6n)^3 ?
The solution to 27(m+2n)^3-(m-6n)^3 is 26m^3+180m^2n+216mn^2+432n^3