How do you factor $12 x^{2} - x y - y^{2}$ $12x^2 - xy - y^2$ ?

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Answer 1 · 2017-01-21T09:50:31

$(y - 4 x) (y + 3 x)$ $(y-4x)(y+3x)$

One way of doing that is by appealing to the homogeneity so making $y = λ x$ $y=lambda x$ and substituting

$12 x^{2} - x y - y^{2} = (12 - λ - λ^{2}) x^{2}$ $12x^2-xy-y^2=(12-lambda-lambda^2)x^2$ or

$(λ + 4) (λ - 3) x^{2} = (λ x - 4 x) (λ x + 3 x) = (y - 4 x) (y + 3 x)$ $(lambda+4)(lambda-3)x^2=(lambda x-4x)(lambda x+3x) = (y-4x)(y+3x)$

How do you factor 12x2−xy−y212x^2 - xy - y^2?