Question

Expand using suitable identities:
${(\frac{1}{4}a-\frac{1}{2}b+1)}^2$

Answer 1

${(\frac{a}{4}-\frac{b}{2}+1)}^2$ using the identity

${(x+y+z)}^2=x^2+y^2+z^2+2xy+2yz+2zx$

where $x=\frac{a}{4},b=\frac{-b}{2},c=1$

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

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