Factorize the following
$(a + b)^{2} + 9 (a + b) + 14$

(a + b + 2) (a + b + 7)

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(a + b + 2) (a + b - 7)

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(a + b - 2) (a + b + 7)

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None of these

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Solution

The correct option is A $(a + b + 2) (a + b + 7)$
$(a + b)^{2} + 9 (a + b) + 14$
Let $a + b = t$
$\begin{matrix} t^{2} + 9 t + 14 t^{2} + 7 t + 2 t + 14 \end{matrix} ∣ ∣ ∣ \begin{matrix} 7 + 2 = 9 7 \times 2 = 14 \end{matrix}$
$t (t + 2) + 7 (t + 2)$
$\begin{matrix} (t + 2) (t + 7) (a + b + 2) (a + b + 7) \end{matrix} {\begin{matrix} s i n c e t = a + b \end{matrix}$

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