State whether the given statement is true or false:
Factorization of $1 - (2 x + 3 y) - 6 (2 x + 3 y)^{2}$ is $(1 - 6 x - 9 y) (1 + 4 x + 6 y)$

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Solution

Let $2 x + 3 y = a$
Factorizing $- 6 a^{2} - a + 1$ ,
Split $a$ as:
$= {- 6 a}^{2} - 3 a + 2 a + 1 = - 3 a (2 a + 1) + 1 (2 a + 1) = (- 3 a + 1) (2 a + 1) = (1 - 6 x - 9 y) (1 + 4 x + 6 y)$
Hence, the given statement is true.

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Factorise : $1 - (2 x + 3 y) - 6 (2 x + 3 y)^{2}$

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