What is (m-2)^3+(m-3)^3 ?

The solution to (m-2)^3+(m-3)^3 is 2m^3-15m^2+39m-35

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simplify (m-2)^3+(m-3)^3

simplify

(m - 2)^{3} + (m - 3)^{3}

2 m^{3} - 15 m^{2} + 39 m - 35

Solution steps

(m - 2)^{3} + (m - 3)^{3}

Expand

(m - 2)^{3} : m^{3} - 6 m^{2} + 12 m - 8

= m^{3} - 6 m^{2} + 12 m - 8 + (m - 3)^{3}

Expand

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

= m^{3} - 6 m^{2} + 12 m - 8 + m^{3} - 9 m^{2} + 27 m - 27

Group like terms

= m^{3} + m^{3} - 6 m^{2} - 9 m^{2} + 12 m + 27 m - 8 - 27

Add similar elements:

m^{3} + m^{3} = 2 m^{3}

= 2 m^{3} - 6 m^{2} - 9 m^{2} + 12 m + 27 m - 8 - 27

Add similar elements:

- 6 m^{2} - 9 m^{2} = - 15 m^{2}

= 2 m^{3} - 15 m^{2} + 12 m + 27 m - 8 - 27

Add similar elements:

12 m + 27 m = 39 m

= 2 m^{3} - 15 m^{2} + 39 m - 8 - 27

Subtract the numbers:

- 8 - 27 = - 35

= 2 m^{3} - 15 m^{2} + 39 m - 35

- 2 - \frac{3}{4}

+ 4

8 \div \frac{2}{5}

- 7.5 \cdot (- 2) \frac{3}{4}

(2 a^{- 2} b^{2} c^{4})^{- 3}