Question

1. use the expression below.

-4b + 8c + 12 - 8b - 2c + 6
part a
simplify the expression.
part b
factor the simplified expression using the gcf.
part c
what is the value of the expression when b = 2 and c = -3?

Explanation:

Step1: Simplify the original expression

Combine like terms: For \( b \) terms: \(-4b - 8b=-12b\); for \( c \) terms: \(8c - 2c = 6c\); for constants: \(12 + 6=18\). So the simplified expression is \(-12b + 6c + 18\).

Step2: Factor using GCF for Part B

Find GCF of \(-12b\), \(6c\), \(18\). The GCF of 12, 6, 18 is 6, and considering the sign, we can take \(-6\) or \(6\). Let's take \(-6\): \(-12b+6c + 18=-6(2b - c - 3)\) (or with GCF 6: \(6(-2b + c + 3)\)).

Step3: Substitute \(b = 2\), \(c=-3\) into simplified expression

Substitute into \(-12b + 6c + 18\): \(-12\times2+6\times(-3)+18=-24-18 + 18=-24\).

Answer:

s:

Part A: \(-12b + 6c + 18\)

Part B: \(6(-2b + c + 3)\) (or \(-6(2b - c - 3)\))

Part C: \(-24\)