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Factorisation of Quadratic Polynomials- Middle Term Splitting

Resolve the f...

Question

Resolve the following quadratic trinomial into factors :
$6 x^{2} - 5 x y - 6 y^{2}$

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Solution

Given : $6 x^{2} - 5 x y - 6 y^{2}$
On splitting the middle term, we get
$6 x^{2} + 4 x y - 9 x y - 6 y^{2}$
$= 2 x (3 x + 2 y) - 3 y (3 x + 2 y)$
$= (2 x - 3 y) (3 x + 2 y)$

Hence, $6 x^{2} - 5 x y - 6 y^{2} = (2 x - 3 y) (3 x + 2 y)$

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Standard IX Mathematics

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