Question

Find and correct the errors in the mathematical statement $(a-4)(a-2)=a^2-8$

Answer 1

Find and correct errors in the given statement:

An equation is a mathematical expression of equality between two algebraic expressions that have equal values.

Given, $(a-4)(a-2)=a^2-8$

On solving L.H.S, we get,

$$\begin{gathered} =(a-4)(a-2) \\ =a(a-2)-4(a-2) \\ =a^2-2a-4a+8 \\ =a^2-6a+8 \end{gathered}$$

But, it is given that R.H.S $=a^2-8$

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

So,for correct statement we need to add $-6a$and need to replace $-8\text{with}+8$in RHS.

Hence, the correct statement is $\mathbf{(}\mathit{a}\mathbf{}\mathbf{-}\mathbf{}\mathbf{4}\mathbf{)}\mathbf{(}\mathit{a}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}{\mathit{a}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{6}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathbf{8}$.