What is factor (m-n)^3-(9-n)^3 ?

The solution to factor (m-n)^3-(9-n)^3 is (m-9)(3n^2-3mn-27n+m^2+9m+81)

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factor (m-n)^3-(9-n)^3

factor

(m - n)^{3} - (9 - n)^{3}

(m - 9) (3 n^{2} - 3 mn - 27 n + m^{2} + 9 m + 81)

Solution steps

(m - n)^{3} - (9 - n)^{3}

Apply Difference of Cubes Formula:

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

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

= ((m - n) - (9 - n)) ((9 - n)^{2} + (9 - n) (m - n) + (m - n)^{2})

Refine

= (m - 9) ((- n + 9)^{2} + (- n + 9) (m - n) + (m - n)^{2})

Factor

9 - n : - (n - 9)

= (m - 9) ((m - n)^{2} - (n - 9) (m - n) + (- n + 9)^{2})

Expand

(m - n)^{2} - (n - 9) (m - n) + (9 - n)^{2} : 3 n^{2} - 3 mn - 27 n + m^{2} + 9 m + 81

= (m - 9) (m^{2} + 9 m - 3 mn + 3 n^{2} + 81 - 27 n)

x^{2} + 4 x + 3

\frac{1}{2} (5) (5)

g - 9 = - 5

6 (z - 1) = 24

\frac{2.24215 \cdot 1 0 ^{- 7}}{2.95} = π r^{2}

What is factor (m-n)^3-(9-n)^3 ?
The solution to factor (m-n)^3-(9-n)^3 is (m-9)(3n^2-3mn-27n+m^2+9m+81)