Ex.14.3 Q18 Factorization - NCERT Maths Class 8

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Question

Find and correct the errors in the statement:

\[\left( {a - 4} \right)\left( {a - 2} \right) = {a^2} - 8\]

Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Solve \(L.H.S.\)

Steps:

\[\begin{align}{L.H.S.}&{ = (a - 4)(a - 2)}\\{}&{ = \left\{ \begin{array}{l}\!\!a\!\times\!a\!+\!\left( { - 2} \right) \!\times\!a +\!\left( { - 4} \right)\!\times\!\!\!\\a + \left[ {( - 4) \times ( - 2)} \right]\end{array} \right\}}\\&{ = {a^2} - 2a - 4a + 8}\\&{ = {a^2} - 6a + 8}\\{L.H.S.}&{ \ne R.H.S.}\end{align}\]

The correct statement is

\[\left( {a - 4} \right)\left( {a - 2} \right) = {a^2} - 6a + 8\]