Factorise:
$7 (x - 2 y)^{2} - 25 (x - 2 y) + 12$

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Solution

Given $7 (x - 2 y)^{2} - 25 (x - 2 y) + 12 P u t x - 2 y = v E q u a t i o n b e c o m e s 7 v^{2} - 25 v + 12 B y s p l i t t i n g t h e m i d d d l e t e r m, w e g e t \Rightarrow 7 v^{2} - 21 v - 4 v + 12 \Rightarrow 7 v (v - 3) - 4 (v - 3) \Rightarrow (7 v - 4) (v - 3) P u t t h e v a l u e b a c k \Rightarrow (7 (x - 2 y) - 4) (x - 2 y - 3) \Rightarrow (7 x - 14 y - 4) (x - 2 y - 3)$
$∴$ $7 (x - 2 y)^{2} - 25 (x - 2 y) + 12$ $=$ $(7x-14y-4)(x-2y -3)$

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