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

The solution to (x-3y)^3+(2x+y)^3 is 9x^3+3x^2y+33xy^2-26y^3

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

simplify

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

9 x^{3} + 3 x^{2} y + 33 x y^{2} - 26 y^{3}

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{3} + 8 x^{3} = 9 x^{3}

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

Add similar elements:

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

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

Add similar elements:

27 x y^{2} + 6 x y^{2} = 33 x y^{2}

= 9 x^{3} + 3 x^{2} y + 33 x y^{2} - 27 y^{3} + y^{3}

Add similar elements:

- 27 y^{3} + y^{3} = - 26 y^{3}

= 9 x^{3} + 3 x^{2} y + 33 x y^{2} - 26 y^{3}

(- 4 - 4) y (8.1)

6 m^{2} + 10 m - 82

125 a^{5} b^{2} - 27 a^{2} b^{5}

(y + 0.2) (y + 0.5)

(x - a)^{9}

What is (x-3y)^3+(2x+y)^3 ?
The solution to (x-3y)^3+(2x+y)^3 is 9x^3+3x^2y+33xy^2-26y^3