Question

Find and correct the errors in the mathematical statement ${\left(z+5\right)}^2=z^2+25$.

Answer 1

Expand $\mathrm{LHS}$ of the expression.

Using identity ${\left(a+b\right)}^2=a^2+b^2+2ab$, expand the expression.

$$\begin{gathered} \Rightarrow {\left(z+5\right)}^2=z^2+5^2+2\left(z\right)\left(5\right) \\ \Rightarrow {\left(z+5\right)}^2=z^2+25+10z \end{gathered}$$

Whereas, $\mathrm{RHS}$ is $z^2+25$

$\Rightarrow \mathrm{LHS}\ne \mathrm{RHS}$

Hence, the correct statement is ${\left(z+5\right)}^2=z^2+25+10z$.