Question

Expand: ${(x+5+\frac{1}{2x})}^2$

Answer 1

Using the identity is $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$.

Given: ${(x+5+\frac{1}{2x})}^2$ we apply the above identity as follows:

${(x+5+\frac{1}{2x})}^2={\left(x\right)}^2+{\left(5\right)}^2+{\left(\frac{1}{2x}\right)}^2+(2\times x\times 5)+(2\times 5\times \frac{1}{2x})+(2\times \frac{1}{2x}\times x)=x^2+25+\frac{1}{{4x}^2}+10x+\frac{5}{x}+1$

$=x^2+26+\frac{1}{{4x}^2}+10x+\frac{5}{x}$

Hence, ${(x+5+\frac{1}{2x})}^2=x^2+26+\frac{1}{{4x}^2}+10x+\frac{5}{x}$.