Factorize :
$3 - 5 x + 5 y - 12 {(x - y)}^{2}$

(3 + 4 x - 4 y) (1 - 3 x + 3 y)

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(3 - 2 x - y) (1 - 3 x + y)

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(3 + 4 x - 4 y) (2 + 3 x + y)

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(3 - 2 x - 4 y) (2 - 3 x + 3 y)

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Solution

The correct option is A $(3 + 4 x - 4 y) (1 - 3 x + 3 y)$
Consider $3 - 5 x + 5 y - 12 {(x - y)}^{2}$
$= 3 - 5 (x - y) - 12 {(x - y)}^{2}$
Let $x - y$ be $a$
Therefore,
$= 3 - 5 a - 12 a^{2}$
$= - 12 a^{2} - 5 a + 3$
$= - 12 a^{2} - 9 a + 4 a + 3$
$= - 3 a (4 a + 3) + 1 (4 a + 3)$
$= (4 a + 3) (1 - 3 a)$
Putting the value of $a$ we get,
$= [4 (x - y) + 3] [1 - 3 (x - y)]$
$= (4 x - 4 y + 3) (1 - 3 x + 3 y)$

Suggest Corrections

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