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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

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