Question

#2 which expression is equivalent to (7ab - 5ac - 9bc) + (8ab - 6ac + 2bc)?
a. 15ab - ac - 7bc
b. 15ab - 11ac + 11bc
c. 15ab + ac - 9bc
d. 15ab + 11ac - 7bc

Explanation:

Step1: Remove parentheses

$(7ab - 5ac - 9bc) + (8ab - 6ac + 2bc) = 7ab - 5ac - 9bc + 8ab - 6ac + 2bc$

Step2: Combine like terms for $ab$

$7ab + 8ab = 15ab$

Step3: Combine like terms for $ac$

$-5ac - 6ac = -11ac$

Step4: Combine like terms for $bc$

$-9bc + 2bc = -7bc$

Step5: Assemble the simplified expression

$15ab - 11ac - 7bc$

Answer:

b. $15ab - 11ac + 11bc$ is incorrect; the correct equivalent expression matches none of the options exactly? No, correction: Wait, Step 3: $-5ac -6ac = -11ac$, Step4: $-9bc +2bc=-7bc$. So the correct expression is $15ab -11ac -7bc$, which is not listed? Wait no, recheck:
Wait original problem: $(7ab -5ac -9bc)+(8ab -6ac +2bc)$
Step1: Group $ab$: $7ab+8ab=15ab$
Step2: Group $ac$: $-5ac -6ac = -11ac$
Step3: Group $bc$: $-9bc +2bc = -7bc$
So the correct expression is $15ab -11ac -7bc$. None of the options match? Wait no, option b is $15ab -11ac +11bc$, option a is $15ab -ac -7bc$. Wait, did I miscalculate?
Wait $-5ac -6ac = -(5+6)ac = -11ac$, correct. $-9bc +2bc = (-9+2)bc=-7bc$, correct. $7ab+8ab=15ab$, correct.

Wait, perhaps a typo in the problem, but based on calculation, the correct simplified form is $15ab -11ac -7bc$. Since this is not listed, but if we recheck, maybe I misread the problem:
Wait the original problem: $(7ab -5ac -9bc)+(8ab -6ac +2bc)$
Yes, that's what's written. So the correct answer should be an option matching $15ab -11ac -7bc$, which is not present. But if we assume a typo, but following calculation: