Question

Find and correct the errors in the following mathematical statements

${\left(2x\right)}^2+4\left(2x\right)+7=2x^2+8x+7$

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,

${\left(2x\right)}^2+4\left(2x\right)+7=2x^2+8x+7$

On solving L.H.S, we get,

$$\begin{gathered} ={\left(2x\right)}^2+4\left(2x\right)+7 \\ =4x^2+8x+7 \end{gathered}$$

But, it is given that R.H.S $=2x^2+8x+7$

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

So, for correct statement we need to replace $2x^2$ with $4x^2$in RHS.

Hence, the correct statement is ${\mathbf{\left(}\mathbf{2}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}\mathbf{}\mathbf{4}\mathbf{\left(}\mathbf{2}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{7}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}{\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{8}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{7}$.