Ex.14.3 Q16 Factorization - NCERT Maths Class 8

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Question

Q16. 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:

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

The correct statement is \(\left( {2a + 3b} \right)\left( {a - b} \right) = 2{a^2} + ab - 3{b^2}\)