Question

Find and correct the errors in the mathematical statement: ${\left(y-3\right)}^2=y^2-9$.

Answer 1

Step 1: Find L.H.S. of the expression.

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

$$\begin{gathered} \Rightarrow {\left(y-3\right)}^2=y^2+3^2-2\left(3\right)\left(y\right) \\ =y^2+9-6y \end{gathered}$$

Step 2: Find R.H.S. of the expression.

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

$\Rightarrow \left(y^2-9\right)=\left(y+3\right)\left(y-3\right)$

Therefore, L.H.S.$\ne$R.H.S.

So,for correct statement we need to add $-6y$and need to replace $-9\text{with}+9$in RHS.

The correct statement is ${\left(y-3\right)}^{\mathbf{2}}\mathbf{=}{\mathit{y}}^{\mathbf{2}}\mathbf{+}\mathbf{9}\mathbf{-}\mathbf{6}\mathit{y}$.