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#