Question

factor the trinomial.
$x^2 - xy - 56y^2$
$(x - 8y)(x + 7y)$

Explanation:

Step1: Identify trinomial form

We have $x^2 - xy - 56y^2$, which fits $x^2 + bx y + cy^2$.

Step2: Find pair for $c=-56$

Find two numbers that multiply to $-56$ and add to $-1$: $-8$ and $7$, since $(-8)\times7=-56$ and $-8+7=-1$.

Step3: Factor the trinomial

Rewrite using the pair, then factor into binomials:
$x^2 - xy - 56y^2 = (x - 8y)(x + 7y)$

Answer:

$(x - 8y)(x + 7y)$