# (a / 4 - b / 2 + 1)2 expand it with suitable identites.

The given expression is

$$\left(\frac{a}{4}-\frac{b}{2}+1\right)^{2}\\ \text { The suitable identity is }(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 x z\\ \left(\frac{a}{4}-\frac{b}{2}+1\right)^{2}\\ =\left(\frac{a}{4}\right)^{2}+2\left(-\frac{b}{2}\right)^{2}+(1)^{2}+2\left(\frac{a}{4}\right)\left(-\frac{b}{2}\right)+2\left(-\frac{b}{2}\right)(1)+2\left(\frac{a}{4}\right)(1)\\ =\frac{a^{2}}{16}+\frac{b^{2}}{4}+1-\frac{a b}{4}-b+\frac{a}{2}$$