Ex.14.3 Q15 Factorization - NCERT Maths Class 8

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Question

Find and correct the errors in the statement:

\[{\left( {z + 5} \right)^2} = {z^2} + 25\]

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:

\[\begin{align}L.H.S.&= {{(z + 5)}^2} \\&= {{(z)}^2} + 2(z)(5) + {(5)}^2 \quad\\ \text{Using identity}\\{(a + b)}^2 &= {a^2} + 2ab + {b^2}\\&= {z^2} + 10z + 25\\L.H.S. &\ne R.H.S.\end{align}\]

The correct statement is \({\left( {z + 5} \right)^2} = {z^2} + 10z + 25\)