Ex.14.3 Q12 Factorization - NCERT Maths Class 8

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Question

Q12. Find and correct the errors in the statement:

\[{\left( {3x + 2} \right)^2} = 3{x^2} + 6x + 4\]

Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Solve \(L.H.S.\)

Steps:

\[\begin{align}L.H.S. = {{(3x + 2)}^2} &= {{(3x)}^2} + 2(3x)(2) + {{(2)}^2 \quad \left[ {\text{Using identity}\;{{(a + b)}^2} = {a^2} + 2ab + {b^2}} \right]}\\&= 9{x^2} + 12x + 4\\L.H.S. &\ne {\rm{ }}R.H.S\end{align}\]

The correct statement is \({\left( {3x{\rm{ }} + {\rm{ }}2} \right)^2} = {\rm{ }}9{x^2}{\rm{ }} + {\rm{ }}12x{\rm{ }} + {\rm{ }}4\)