How do you factor the trinomial $x^2-8xy-9y^2$ ?

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Answer 1 · 2015-12-26T21:58:45

Factor by grouping to find:

$x^2-8xy-9y^2=(x-9y)(x+y)$

You can split the middle term and factor by grouping as follows:

$x^2-8xy-9y^2$

$=x^2+xy-9xy-9y^2$

$=(x^2+xy)-(9xy+9y^2)$

$=x(x+y)-9y(x+y)$

$=(x-9y)(x+y)$

The choice of split comes from finding a pair of factors of $9$ which differ by $8$ , namely $1$ and $9$ .

How do you factor the trinomial x^2-8xy-9y^2x^2-8xy-9y^2?