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# Ex.14.3 Q16 Factorization - NCERT Maths Class 8

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## Question

Find and correct the errors in the statement:

$\left( {2a + 3b} \right)\left( {a - b} \right) = 2{a^2} - 3{b^2}$

## Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Solve $$L.H.S.$$

Steps:

\begin{align}{L.H.S.}&{ = (2a + 3b)(a - b)}\\{}&={\left( \begin{array}{l} 2a \times a - 2a \times b + \\3b \times a - 3b \times b\end{array} \right)}\\{}&{ = 2{a^2} - 2ab + 3ab - 3{b^2}}\\{}&{ = 2{a^2} + ab - 3{b^2}}\\{L.H.S.}&{ \ne {\rm{R}}.{\rm{H}}.{\rm{S}}.}\end{align}

The correct statement is

$\left( {2a + 3b} \right)\left( {a - b} \right) = 2{a^2} + ab - 3{b^2}$

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