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

The solution to (x+y+z)^3-x^3-y^3-z^3 is 3x^2y+3x^2z+3xz^2+3yz^2+3xy^2+3y^2z+6xyz

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

simplify

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

3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + 3 y^{2} z + 6 x yz

Solution steps

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

Expand

(x + y + z)^{3} : x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + z^{3} + 3 y^{2} z + 6 x yz + y^{3}

= x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + z^{3} + 3 y^{2} z + 6 x yz + y^{3} - x^{3} - y^{3} - z^{3}

Group like terms

= x^{3} - x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + z^{3} - z^{3} + 3 y^{2} z + 6 x yz + y^{3} - y^{3}

Add similar elements:

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

= 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + z^{3} - z^{3} + 3 y^{2} z + 6 x yz + y^{3} - y^{3}

Add similar elements:

z^{3} - z^{3} = 0

= 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + 3 y^{2} z + 6 x yz + y^{3} - y^{3}

Add similar elements:

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

= 3 x^{2} y + 3 x^{2} z + 3 x z^{2} + 3 y z^{2} + 3 x y^{2} + 3 y^{2} z + 6 x yz

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

6 x^{3} \cdot 4 x^{2}

e^{x - l n (x)}

\frac{7}{5 2}

\frac{2}{3} + \frac{1}{2} + \frac{3}{4}

What is (x+y+z)^3-x^3-y^3-z^3 ?
The solution to (x+y+z)^3-x^3-y^3-z^3 is 3x^2y+3x^2z+3xz^2+3yz^2+3xy^2+3y^2z+6xyz