Question

what is the factored form of the following expression? x^2 - 4xy - 21y^2

Answer 1

(x - 7y) (x + 3y)

Answer 2

@Lingey OpenStudy values the Learning process - not the ‘Give you an answer’ process.
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@ThatBoyIsANinja when you see that you have 2 different variables in the trinomial, with the x^2 in the first term, the y^2 in the last term, and the xy in the middle term, then you know that the factoring will take the form:

\(\large (ax\pm by)(cx\pm dy)\)

So treat it just like factoring a trinomial that only has x in it, except that you'll need to include a y variable in each of the 2nd terms. E.g., you can factor just like you would factor \(\large x^2 - 4x - 21=(???)(???)\) but then just include a y in the last term of each binomial factor.