SOLUTION: how do i factor a trinomial such as: xsquared

SOLUTION: how do i factor a trinomial such as: xsquared - 14xy -51ysquared

Question 423330: how do i factor a trinomial such as: xsquared - 14xy -51ysquared
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your trinomial is:

x^2 - 14xy - 51y^2

your factors will be in the form of:

(x-ay) * (x+by)

multiply these factors together and you will get:

x^2 + bxy - axy - aby^2

combine like terms to get:

x^2 + (b-a)xy - aby^2

since your original equation is:

x^2 - 14xy -51y^2, this mans that:

(b-a) must be equal to -14
ab must be equal to 51

it just so happens that if a = 17 and b = 3, then you will get:

x^2 + (3-17)xy - (3*17)y^2 which will become:

x^2 - 14xy - 51y^2

so, you need to make a = 17 and b = 3

the general form of your factors is:

(x-ay) * (x+by)

substitute 17 for a and 3 for b to get:

(x-17y) * (x+3y)

multiply these factors together to get:

x^2 + 3xy - 17xy - 51y^2

combine like terms to get:

x^2 - 14xy - 51y^2

your factors are:

(x-17y) * (x+3y)

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