Solve 1/2(x+y+z)^2

Evaluate

\frac{1}{2} (x + y + z)^{2}

Use (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 ab + 2 a c + 2 b c to expand the expression

\frac{1}{2} (x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz)

Apply the distributive property

\frac{1}{2} x^{2} + \frac{1}{2} y^{2} + \frac{1}{2} z^{2} + \frac{1}{2} \times 2 x y + \frac{1}{2} \times 2 x z + \frac{1}{2} \times 2 yz

Multiply the numbers

More Steps

\frac{1}{2} x^{2} + \frac{1}{2} y^{2} + \frac{1}{2} z^{2} + x y + \frac{1}{2} \times 2 x z + \frac{1}{2} \times 2 yz

Multiply the numbers

More Steps

\frac{1}{2} x^{2} + \frac{1}{2} y^{2} + \frac{1}{2} z^{2} + x y + x z + \frac{1}{2} \times 2 yz

Solution

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\frac{1}{2} x^{2} + \frac{1}{2} y^{2} + \frac{1}{2} z^{2} + x y + x z + yz

Simplify the expression