Question

1. which expression is equivalent to \\(5mn - 6mp - 3np + 9mn + 10mp + 8np\\)?

a. \\(14mn - 4mp + 5np\\)
b. \\(14mn + mp - 5np\\)
c. \\(14mn + 4mp - 5np\\)
d. \\(14mn + 4mp + 5np\\)

Explanation:

Step1: Remove parentheses

$(5mn - 6mp - 3np) + (9mn + 10mp + 8np) = 5mn - 6mp - 3np + 9mn + 10mp + 8np$

Step2: Combine like terms for $mn$

$5mn + 9mn = 14mn$

Step3: Combine like terms for $mp$

$-6mp + 10mp = 4mp$

Step4: Combine like terms for $np$

$-3np + 8np = 5np$

Step5: Combine all simplified terms

$14mn + 4mp + 5np$

Answer:

d. $14mn + 4mp + 5np$