Question

Expand ${\left[\frac{1}{4}a-\frac{1}{2}b+1\right]}^2$

Answer 1

Expand

$\left[\right(\frac{a}{4}+1)-\frac{b}{2}{]}^2=(\frac{a}{4}+1{)}^2-2(\frac{a}{4}+1)\left(\frac{b}{2}\right)+\frac{b^2}{4}$

$=\frac{a^2}{16}+\frac{2a}{4}+1-2[\frac{ab}{8}+\frac{b}{2}]+\frac{b^2}{4}$

$=\frac{a^2}{16}+\frac{2a}{4}+1-\frac{ab}{4}-b+\frac{b^2}{4}$

$\left[\right(\frac{a}{4}+1)-\frac{b}{2}{]}^2=\frac{a^2}{16}+\frac{b^2}{4}+\frac{9}{2}-b-\frac{ab}{4}+1$