Ex.14.3 Q17 Factorization - NCERT Maths Class 8

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Question

Find and correct the errors in the statement:

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

Text Solution

What is known?

Incorrect mathematical statement.

What is unknown?

Correct mathematical statement.

Reasoning:

Solve \(L.H.S.\)

Steps:

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

The correct statement is

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