What is factor (2a-b)^3-(3b-a)^3 ?

The solution to factor (2a-b)^3-(3b-a)^3 is (3a-4b)(3a^2-3ab+7b^2)

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factor (2a-b)^3-(3b-a)^3

factor

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

(3 a - 4 b) (3 a^{2} - 3 ab + 7 b^{2})

Solution steps

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

Apply Difference of Cubes Formula:

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

(2 a - b)^{3} - (3 b - a)^{3} = ((2 a - b) - (3 b - a)) ((2 a - b)^{2} + (3 b - a) (2 a - b) + (3 b - a)^{2})

= ((2 a - b) - (3 b - a)) ((3 b - a)^{2} + (3 b - a) (2 a - b) + (2 a - b)^{2})

Refine

= (3 a - 4 b) ((2 a - b)^{2} + (3 b - a) (2 a - b) + (3 b - a)^{2})

Expand

(2 a - b)^{2} + (3 b - a) (2 a - b) + (3 b - a)^{2} : 3 a^{2} - 3 ab + 7 b^{2}

= (3 a - 4 b) (3 a^{2} - 3 ab + 7 b^{2})

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What is factor (2a-b)^3-(3b-a)^3 ?
The solution to factor (2a-b)^3-(3b-a)^3 is (3a-4b)(3a^2-3ab+7b^2)