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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorize: 7x...

Question

Factorize:

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

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Solution

$7 (x - 2 y)^{2} - 25 (x - 2 y) + 12$
Let $x - 2 y = a$
Now, $7 a^{2} - 25 a + 12$
$∵ 7 \times 12 = 84$
$∴ 84 = - 21 \times (- 4)$
So, $- 25 = - 21 - 4$
$= 7 a^{2} - 21 a - 4 a + 12$
$= 7 a (a - 3) - 4 (a - 3)$
$= (a - 3) (7 a - 4)$
$= (x - 2 y - 3) (7 x - 14 y - 4)$

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Factorisation of Quadratic Polynomials- Middle Term Splitting

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