Question

Find and correct the errors in the mathematical statement: $(2a+3b)(a-b)=2a^2-3b^2$

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, $(2a+3b)(a-b)=2a^2-3b^2$

On solving L.H.S, we get,

$$\begin{gathered} =(2a+3b)(a-b) \\ =2a(a-b)+3b(a-b) \\ =2a^2-2ab+3ab-3b^2 \\ =2a^2+ab-3b^2 \end{gathered}$$

But, it is given that R.H.S $=2a^2-3b^2$

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

So,for correct statement we need to add $+ab$ in RHS.

Hence, the correct statement is $\mathbf{(}\mathbf{2}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}\mathit{b}\mathbf{)}\mathbf{(}\mathit{a}\mathbf{}\mathbf{-}\mathbf{}\mathit{b}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}{\mathit{a}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathit{a}\mathit{b}\mathbf{}\mathbf{-}\mathbf{}\mathbf{3}{\mathit{b}}^{\mathbf{2}}$.