Ex.14.3 Q14 Factorization - NCERT Maths Class 8

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Question

Find and correct the errors in the statement:

\[{(y - 3)^2} = {y^2} - 9\]

Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Use identity \({(a - b)^2} = {a^2} - 2ab + {b^2}\)

Steps:

\[\begin{align}L.H.S. &= {(y - 3)}^2 \\&= {{(y)}^2} - 2(y)(3) + {{(3)}^2} \quad \\\text {Using identity}\\(a - b)^2 &= {a^2} - 2ab + {b^2}\\&= {y^2} - 6y + 9\\L.H.S. &\ne R.H.S.\end{align}\]

The correct statement is

\[{(y - 3)^2} = {y^2} - 6y + 9\]