Question:
Find the value
$7(x-2 y)^{2}-25(x-2 y)+12$
Solution:
Let $x-2 y=P$
$=7 P^{2}-25 P+12$
Splitting the middle term,
$=7 P^{2}-21 P-4 P+12$
$=7 P(P-3)-4(P-3)$
$=(P-3)(7 P-4)$
Substituting P = x - 2y
$=(x-2 y-3)(7(x-2 y)-4)$
$=(x-2 y-3)(7 x-14 y-4)$
$\therefore 7(x-2 y)^{2}-25(x-2 y)+12=(x-2 y-3)(7 x-14 y-4)$
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