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

The solution to (2x-y)^3-(3x-y)^3 is -19x^3+15x^2y-3xy^2

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simplify (2x-y)^3-(3x-y)^3

simplify

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

- 19 x^{3} + 15 x^{2} y - 3 x y^{2}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

8 x^{3} - 27 x^{3} = - 19 x^{3}

= - 19 x^{3} - 12 x^{2} y + 27 x^{2} y + 6 x y^{2} - 9 x y^{2} - y^{3} + y^{3}

Add similar elements:

- 12 x^{2} y + 27 x^{2} y = 15 x^{2} y

= - 19 x^{3} + 15 x^{2} y + 6 x y^{2} - 9 x y^{2} - y^{3} + y^{3}

Add similar elements:

6 x y^{2} - 9 x y^{2} = - 3 x y^{2}

= - 19 x^{3} + 15 x^{2} y - 3 x y^{2} - y^{3} + y^{3}

Add similar elements:

- y^{3} + y^{3} = 0

= - 19 x^{3} + 15 x^{2} y - 3 x y^{2}

\frac{( 8 x - 24 )}{( 2 x ^{2} - x - 15 )}

\frac{1}{( 1 + a ^{y - x} )} + \frac{1}{( 1 + a ^{x - y} )}

\frac{b \cdot ( 2 \frac{a}{36} ) ^{3}}{( 4 \frac{a}{b} ) ^{2}}

(- 1 x^{2} - 3) - (- 1.1)

(\frac{2}{x - 1})^{3} - (\frac{2}{x - 1})^{2} - 2 (\frac{2}{x - 1}) - 1

What is (2x-y)^3-(3x-y)^3 ?
The solution to (2x-y)^3-(3x-y)^3 is -19x^3+15x^2y-3xy^2