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\frac{2z_{1}^{2}}{2}+\frac{z^{2}}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply z_{1}^{2} times \frac{2}{2}.
\frac{2z_{1}^{2}+z^{2}}{2}
Since \frac{2z_{1}^{2}}{2} and \frac{z^{2}}{2} have the same denominator, add them by adding their numerators.
\frac{2z_{1}^{2}+z^{2}}{2}
Factor out \frac{1}{2}.