Factorise the following:
$a^{2} - 5 a b - 36 b^{2}$

(a - 2 b) (a + 9 b)

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(a + 4 b) (a - 9 b)

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(a + 5 b) (a - 2 b)

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(a - 4 b) (a + 5 b)

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Solution

The correct option is B $(a + 4 b) (a - 9 b)$
$a^{2} - 5 a b - 36 b^{2}$
$= a^{2} - 9 a b + 4 a b - 36 b^{2}$
$= a (a - 9 b) + 4 b (a - 9 b)$
$= (a - 9 b) (a + 4 b)$

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∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a + b & a + 2 b & a + 3 b a + 2 b & a + 3 b & a + 4 b a + 4 b & a + 5 b & a + 6 b \end{matrix} ∣ ∣ ∣ ∣ =

a^{2} + a b + 9 a + 9 b

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