Question: Factorise:
$z^{2}+z+\frac{1}{4}$
Solution:
We have:
$z^{2}+z+\frac{1}{4}=z^{2}+2 \times z \times \frac{1}{2} \times\left(\frac{1}{2}\right)^{2}$
$=\left(z+\frac{1}{2}\right)^{2}$
$\therefore z^{2}+z+\frac{1}{4}=\left(z+\frac{1}{2}\right)^{2}$
