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

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Answer 1 · 2015-07-06T11:37:06

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

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

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

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

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

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

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

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

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

How do you factor 3x^2 +10xy -25y^23x^2 +10xy -25y^2?