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

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

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

factor

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

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

Solution steps

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

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

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

Expand

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

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

Simplify

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

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

Rewrite as

= 3 x^{2} y + 3 x^{2} z + 3 x y^{2} + 3 x z^{2} + 3 \cdot 2 x yz + 3 y z^{2} + 3 y^{2} z

Factor out common term

3

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

34.46 + \frac{50}{40}

9 x^{2} - 42 x + 49 = 0

3 x + 2 = x - 7

(\frac{6}{7})^{0}

x + \frac{x}{3} \leq 20

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