Question
Factorise:
$7(x - 2y)^2 - 25(x - 2y) + 12$
$7(x - 2y)^2 - 25(x - 2y) + 12$
✓
Answer
Let $x-2 y=z$
Then, $7( x -2 y )^2-25( x -2 y )+12$
$=7 z^2-25 z+12$
$=7 z^2-21 z-4 z+12$
$=7 z(z-3)-4(z-3)$
$=(z-3)(7 z-4)$
Now replace $z$ by ( $x-2 y$ ), we get
$7(x-2 y)^2-25(x-2 y)+12$
$=(x-2 y-3)[7(x-2 y)-4]$
$=(x-2 y-3)(7 x-14 y-4)$
Then, $7( x -2 y )^2-25( x -2 y )+12$
$=7 z^2-25 z+12$
$=7 z^2-21 z-4 z+12$
$=7 z(z-3)-4(z-3)$
$=(z-3)(7 z-4)$
Now replace $z$ by ( $x-2 y$ ), we get
$7(x-2 y)^2-25(x-2 y)+12$
$=(x-2 y-3)[7(x-2 y)-4]$
$=(x-2 y-3)(7 x-14 y-4)$
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