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Question

Factorize the given polynomial expression
$$7{(x-2y)}^{2}-25(x-2y)+12$$


Solution

Given thar,
$$7{(x-2y)}^{2}-25(x-2y)+12$$

$$let x-2y=a$$
$$\therefore 7{(x-2y)}^{2}-25(x-2y)+12=7a^2-25a+12$$

$$=7a^2-21a-4a+12$$
$$=7a(a-3)-4(a-3)$$
$$=(a-3)(7a-4)$$
$$=(x-2y-3)(7(x-2y)-4)$$                                       $$[\because a=x-2y]$$
$$=(x-2y-3)(7x-14y-4)$$        

$$\therefore 7{(x-2y)}^{2}-25(x-2y)+12= (x-2y-3)(7x-14y-4)$$

Mathematics

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