# 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

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