Question

factor the trinomial.
$x^2 - 5xy + 6y^2$

Explanation:

Step1: Identify target pair for factoring

We need two terms that multiply to $6y^2$ and add to $-5y$.

Step2: Split the middle term

Rewrite $-5xy$ as $-2xy - 3xy$:
$x^2 - 2xy - 3xy + 6y^2$

Step3: Factor by grouping

Group first/second and third/fourth terms:
$(x^2 - 2xy) + (-3xy + 6y^2)$
Factor out common terms:
$x(x - 2y) - 3y(x - 2y)$

Step4: Factor out shared binomial

Extract $(x - 2y)$ from both terms:
$(x - 2y)(x - 3y)$

Answer:

$(x - 2y)(x - 3y)$