Question

an expression is shown.
-15y - 40
create 2 equivalent expressions that show
the product of two factors.

Explanation:

Step1: Find GCD of coefficients

GCD of 15 and 40 is 5. Factor out -5:
$-5(3y + 8)$

Step2: Factor out -1 (optional, use GCD -5 again)

Factor out -5 again (or use another GCD, like -1*5). Wait, another way: factor out -5 first, then factor out 5 with sign. Wait, let's do another GCD. GCD of 15 and 40 is also 5, but factor out -5 and then factor out 5? No, better: find another common factor. Wait, -15y -40 can also be factored by -5 (as above) and also by 5 with a negative sign. Wait, let's do:

First equivalent: factor out -5: $-5(3y + 8)$

Second equivalent: factor out 5 (but note the signs). Wait, -15y -40 = 5(-3y - 8) (since 5(-3y) = -15y and 5(-8) = -40). Wait, let's check:

5*(-3y -8) = -15y -40. Yes. And -5(3y +8) = -15y -40. So two equivalent expressions are $-5(3y + 8)$ and $5(-3y - 8)$.

Answer:

Two equivalent expressions are $\boldsymbol{-5(3y + 8)}$ and $\boldsymbol{5(-3y - 8)}$ (other valid expressions are also possible, e.g., $-1(15y + 40)$ but that's a single factor with -1, but the problem says product of two factors, so two factors. Wait, $-1(15y + 40)$ is product of -1 and (15y +40), so that's also valid. But the first two are better with GCD 5 and -5).