How do you factor $y^{2} + 2 x y - 63 x^{2}$ $y^2 + 2xy - 63x^2$ ?

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Answer 1 · 2015-05-17T12:26:33

Consider $(y + a x) (y - b x) = y^{2} + (a - b) y - (a b) x^{2}$ $(y+ax)(y-bx) = y^2+(a-b)y-(ab)x^2$

Comparing coefficients with our target quadratic, we are looking for $a$ $a$ and $b$ $b$ such that $a - b = 2$ $a - b = 2$ and $a b = 63$ $ab=63$ .

Well $63 = 9 \cdot 7$ $63 = 9*7$ and $9 - 7 = 2$ $9-7 = 2$

Hence $y^{2} + 2 x y - 63 x^{2} = (y + 9 x) (y - 7 x)$ $y^2+2xy-63x^2 = (y+9x)(y-7x)$

How do you factor y2+2xy−63x2 y^2 + 2xy - 63x^2 ?