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

The solution to factor (m-2)^3+(m-3)^3 is (2m-5)(m^2-5m+7)

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

factor

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

(2 m - 5) (m^{2} - 5 m + 7)

Solution steps

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

Apply Sum of Cubes Formula:

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

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

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

Refine

= (2 m - 5) ((m - 2)^{2} - (m - 3) (m - 2) + (m - 3)^{2})

Expand

(m - 2)^{2} - (m - 3) (m - 2) + (m - 3)^{2} : m^{2} - 5 m + 7

= (2 m - 5) (m^{2} - 5 m + 7)

e^{3} - e^{2}

15 a t + 3 b t + 5 a s + b s

\cdot (- 5)

+ (- 4)

3 a c + 2 b c - 6 a d - 4 b d

What is factor (m-2)^3+(m-3)^3 ?
The solution to factor (m-2)^3+(m-3)^3 is (2m-5)(m^2-5m+7)