What is factor (2x-y)^3-(3x+y)^3 ?

The solution to factor (2x-y)^3-(3x+y)^3 is (-x-2y)(19x^2+xy+y^2)

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factor (2x-y)^3-(3x+y)^3

factor

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

(- x - 2 y) (19 x^{2} + x y + y^{2})

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

(2 x - y)^{2} + (2 x - y) (3 x + y) + (3 x + y)^{2} : 19 x^{2} + x y + y^{2}

= (- x - 2 y) (19 x^{2} + x y + y^{2})

tan (4 x + 20) cot (x + 8 0^{\circ})

a e^{- x} + b e^{- x + 4 s i n (x)}

(- 8 - 6 i)^{\frac{1}{2}}

e^{l n (y + 2)}

x a + 3 x + x^{2} + 2 a + 6 + 2 x

What is factor (2x-y)^3-(3x+y)^3 ?
The solution to factor (2x-y)^3-(3x+y)^3 is (-x-2y)(19x^2+xy+y^2)