Question

1. use the expression $8a + 16c$.

part a
factor the expression using the gcf.
$4a + 4c$
part b
what is the value of the expression when $a = -5$ and $c = -1$?
$4 \times -5 + 4 \times -1$
$-20 - 4$

Explanation:

Step1: Identify GCF of 8 and 16

The factors of 8 are \(1, 2, 4, 8\), and factors of 16 are \(1, 2, 4, 8, 16\). The GCF is 8.

Step2: Factor the expression

Using the distributive property \(ab + ac = a(b + c)\), factor out 8 from \(8a + 16c\):
\(8a + 16c = 8(a + 2c)\)

Step3: Substitute values for Part B

Given \(a = -5\) and \(c = -1\), substitute into \(8a + 16c\):
\(8(-5) + 16(-1)\)

Step4: Calculate each term

\(8(-5) = -40\) and \(16(-1) = -16\)

Step5: Sum the terms

\(-40 + (-16) = -40 - 16 = -56\)

Answer:

Part A: \(8(a + 2c)\)
Part B: \(-56\)