Question

simplify the expression.
4b b + 6 c + 6
part b
factor the simplified expression using the gcf.
2(-2b + c + 3)
3(-2b + c + 3)
4(-2b + c + 3)
6(-2b + c + 3)
part c
what is the value of the expression when b = 2 and c = -3?

Explanation:

Part B

To factor the simplified expression using GCF, we first assume the simplified expression from Part A (though not fully shown, we analyze the options). The GCF of the terms in the expression (after simplifying, likely -6b + 3c + 9 or similar) should be determined. Let's check the options:

• Option 2(-2b + c + 3): 2(-2b)= -4b, 2c=2c, 2*3=6. Doesn't match if original had -6b etc.
• Option 3(-2b + c + 3): 3(-2b)= -6b, 3c=3c, 3*3=9. If the simplified expression is -6b + 3c + 9, GCF is 3. So this works.
• Option 4(-2b + c + 3): 4*(-2b)= -8b, not matching.
• Option 6(-2b + c + 3): 6*(-2b)= -12b, not matching.

So the correct factoring is with GCF 3.

Step1: Identify the simplified expression (from Part B, we can use the factored form or assume the simplified linear expression). Let's use the factored form 3(-2b + c + 3) or the original simplified (let's also check by plugging into the original or simplified). First, let's find the simplified expression from Part A (assuming the original was 4b - 10b + 6c + 6? Wait, maybe the original expression before simplifying was 4b - 10b + 6c + 6? Wait, no, the first part was "4b" and then "b + 6 c + 6" – maybe a typo, but from Part B, the factored form is 3(-2b + c + 3), so the simplified expression is -6b + 3c + 9.

Step2: Substitute b = 2 and c = -3 into the simplified expression. Let's use the simplified expression: -6b + 3c + 9.

Substitute b = 2: -6*(2) = -12.
Substitute c = -3: 3*(-3) = -9.
Now add them: -12 + (-9) + 9.

Step3: Calculate the value. -12 -9 +9 = -12.

Alternatively, use the factored form: 3(-2b + c + 3). Substitute b=2, c=-3: 3(-2*2 + (-3) + 3) = 3(-4 -3 +3) = 3(-4) = -12.

Answer:

B. 3(-2b + c + 3)

Part C