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