How do you factor 3x2+10xy25y2?

1 Answer
Jul 6, 2015

3x2+10xy25y2=(3x5y)(x+5y)

Explanation:

If 3x2+10xy25y2 has factors with integer coefficients, then they will take the form:

3x2+10xy25y2=(3x+ay)(x+by)

=3x2+(3b+a)xy+aby2

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