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Factorisation of Quadratic Polynomials- Middle Term Splitting

Resolve the f...

Question

Resolve the following quadratic trinomial into factors :
$12 x^{2} - 17 x y + 6 y^{2}$

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Solution

Given : $12 x^{2} - 17 x y + 6 y^{2}$
On splitting the middle term, we get
$12 x^{2} - 9 x y - 8 x y + 6 y^{2}$
$= 3 x (4 x - 3 y) - 2 y (4 x - 3 y)$
$= (3 x - 2 y) (4 x - 3 y)$

Hence, $12 x^{2} - 17 x y + 6 y^{2} = (3 x - 2 y) (4 x - 3 y)$

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Standard IX Mathematics

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