What is (3x-2y)^3-(5y+3x)^3 ?

The solution to (3x-2y)^3-(5y+3x)^3 is -189x^2y-189xy^2-133y^3

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simplify (3x-2y)^3-(5y+3x)^3

simplify

(3 x - 2 y)^{3} - (5 y + 3 x)^{3}

- 189 x^{2} y - 189 x y^{2} - 133 y^{3}

Solution steps

(3 x - 2 y)^{3} - (5 y + 3 x)^{3}

Expand

(3 x - 2 y)^{3} : 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3}

= 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - (5 y + 3 x)^{3}

Expand

- (5 y + 3 x)^{3} : - 125 y^{3} - 225 x y^{2} - 135 x^{2} y - 27 x^{3}

= 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 8 y^{3} - 125 y^{3} - 225 x y^{2} - 135 x^{2} y - 27 x^{3}

Add similar elements:

- 8 y^{3} - 125 y^{3} = - 133 y^{3}

= 27 x^{3} - 54 x^{2} y + 36 x y^{2} - 133 y^{3} - 225 x y^{2} - 135 x^{2} y - 27 x^{3}

Group like terms

= 27 x^{3} - 27 x^{3} - 54 x^{2} y - 135 x^{2} y + 36 x y^{2} - 225 x y^{2} - 133 y^{3}

Add similar elements:

27 x^{3} - 27 x^{3} = 0

= - 54 x^{2} y - 135 x^{2} y + 36 x y^{2} - 225 x y^{2} - 133 y^{3}

Add similar elements:

- 54 x^{2} y - 135 x^{2} y = - 189 x^{2} y

= - 189 x^{2} y + 36 x y^{2} - 225 x y^{2} - 133 y^{3}

Add similar elements:

36 x y^{2} - 225 x y^{2} = - 189 x y^{2}

= - 189 x^{2} y - 189 x y^{2} - 133 y^{3}

3 w - 3 - (2 w + 2) = 8

2 x^{2} = 9 x + 56

x^{2} - 3 x - 40 > 0

\frac{x ^{2} + x}{7} = 8

(x - 5) (x + 8) = 0

What is (3x-2y)^3-(5y+3x)^3 ?
The solution to (3x-2y)^3-(5y+3x)^3 is -189x^2y-189xy^2-133y^3