How do you factor $3 x^{2} + 10 x y - 25 y^{2}$ $3x^2 +10xy -25y^2$ ?

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Answer 1 · 2015-07-06T11:37:06

$3 x^{2} + 10 x y - 25 y^{2} = (3 x - 5 y) (x + 5 y)$ $3x^2+10xy-25y^2 = (3x-5y)(x+5y)$

If $3 x^{2} + 10 x y - 25 y^{2}$ $3x^2+10xy-25y^2$ has factors with integer coefficients, then they will take the form:

$3 x^{2} + 10 x y - 25 y^{2} = (3 x + a y) (x + b y)$ $3x^2+10xy-25y^2 = (3x+ay)(x+by)$

$= 3 x^{2} + (3 b + a) x y + a b y^{2}$ $= 3x^2+(3b+a)xy+aby^2$

Since $a b = - 25$ $ab=-25$ , the possible $(a, b)$ $(a, b)$ values are:

$(- 25, 1)$ $(-25, 1)$ , $(- 5, 5)$ $(-5, 5)$ , $(- 1, 25)$ $(-1, 25)$ , $(1, - 25)$ $(1, -25)$ , $(5, - 5)$ $(5, -5)$ , $(25, - 1)$ $(25, -1)$

These give values for $3 b + a$ $3b+a$ of:

$- 22$ $-22$ , $10$ $10$ , $74$ $74$ , $- 74$ $-74$ , $- 10$ $-10$ , $22$ $22$

So choose $a = - 5$ $a=-5$ and $b = 5$ $b=5$ to get the correct coefficient of $x y$ $xy$

How do you factor 3x2+10xy−25y23x^2 +10xy -25y^2?