Question
Factorize: $7(x - 2y)^2 - 25(x - 2y) + 12$
✓
Answer
Let $x - 2y = P = 7P^2 - 25P + 12$
Splitting the middle term, $= 7P^2 - 21P - 4P + 12$
$= 7P(P - 3) - 4(P - 3) = (P - 3)(7P - 4)$
Substituting $P = x - 2y = (x - 2y - 3)(7(x - 2y) - 4) $
$= (x - 2y - 3)(7x - 14y - 4)$
$\therefore$$ 7(x - 2y)^2 - 25(x - 2y) + 12$
$ = (x - 2y - 3)(7x - 14y - 4)$
Splitting the middle term, $= 7P^2 - 21P - 4P + 12$
$= 7P(P - 3) - 4(P - 3) = (P - 3)(7P - 4)$
Substituting $P = x - 2y = (x - 2y - 3)(7(x - 2y) - 4) $
$= (x - 2y - 3)(7x - 14y - 4)$
$\therefore$$ 7(x - 2y)^2 - 25(x - 2y) + 12$
$ = (x - 2y - 3)(7x - 14y - 4)$
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