What is 8(x+y)^3-27(x-y)^3 ?

The solution to 8(x+y)^3-27(x-y)^3 is -19x^3+105x^2y-57xy^2+35y^3

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simplify 8(x+y)^3-27(x-y)^3

simplify

8 (x + y)^{3} - 27 (x - y)^{3}

- 19 x^{3} + 105 x^{2} y - 57 x y^{2} + 35 y^{3}

Solution steps

8 (x + y)^{3} - 27 (x - y)^{3}

Expand

8 (x + y)^{3} : 8 x^{3} + 24 x^{2} y + 24 x y^{2} + 8 y^{3}

= 8 x^{3} + 24 x^{2} y + 24 x y^{2} + 8 y^{3} - 27 (x - y)^{3}

Expand

- 27 (x - y)^{3} : - 27 x^{3} + 81 x^{2} y - 81 x y^{2} + 27 y^{3}

= 8 x^{3} + 24 x^{2} y + 24 x y^{2} + 8 y^{3} - 27 x^{3} + 81 x^{2} y - 81 x y^{2} + 27 y^{3}

Group like terms

= 8 x^{3} - 27 x^{3} + 24 x^{2} y + 81 x^{2} y + 24 x y^{2} - 81 x y^{2} + 8 y^{3} + 27 y^{3}

Add similar elements:

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

= - 19 x^{3} + 24 x^{2} y + 81 x^{2} y + 24 x y^{2} - 81 x y^{2} + 8 y^{3} + 27 y^{3}

Add similar elements:

24 x^{2} y + 81 x^{2} y = 105 x^{2} y

= - 19 x^{3} + 105 x^{2} y + 24 x y^{2} - 81 x y^{2} + 8 y^{3} + 27 y^{3}

Add similar elements:

24 x y^{2} - 81 x y^{2} = - 57 x y^{2}

= - 19 x^{3} + 105 x^{2} y - 57 x y^{2} + 8 y^{3} + 27 y^{3}

Add similar elements:

8 y^{3} + 27 y^{3} = 35 y^{3}

= - 19 x^{3} + 105 x^{2} y - 57 x y^{2} + 35 y^{3}

(3 x^{3})^{2} \cdot 4 x^{3}

(\frac{3 p + q}{3})^{2}

24 \frac{n ^{2}}{n} + 32 \frac{n}{n} + \frac{12}{n}

(x^{3} y^{3} - 6) (x^{3} y^{3} - 6)

(2 l + 5 m)^{3}

What is 8(x+y)^3-27(x-y)^3 ?
The solution to 8(x+y)^3-27(x-y)^3 is -19x^3+105x^2y-57xy^2+35y^3