Question

Expand each of the following, using suitable identities
${(\frac{a}{4}-\frac{b}{2}+1)}^2$

Answer 1

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

Suitable identities is $(x+y+z{)}^2=x^2+y^2+z^2+2xy+2yz+2xz$

So ${(\frac{a}{4}-\frac{b}{2}+1)}^2$

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

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