Question

Consider the expression

24
x
+
18
y
−
36
24x+18y−36.
Use the distributive property to generate an expression with 2 as a common factor.

Answer 1

To factor the expression \( 24x + 18y - 36 \) using the distributive property, we first look for the greatest common factor (GCF) of the coefficients: 24, 18, and -36.

The GCF of these numbers is 6. We can factor out 6 from each term:

\[
24x = 6 \times 4x
\]
\[
18y = 6 \times 3y
\]
\[
-36 = 6 \times -6
\]

Now, we can rewrite the original expression by factoring out 6:

\[
24x + 18y - 36 = 6(4x + 3y - 6)
\]

Next, we want to use 2 as a common factor instead. We can notice that 6 itself can be written as \(2 \times 3\):

Thus, we can write \( 6(4x + 3y - 6) \) as:

\[
= 2 \times 3(4x + 3y - 6)
\]

However, if we want \(2\) to be the common factor only, we'll factor out \(2\) instead:

\[
24x = 2 \times 12x
\]
\[
18y = 2 \times 9y
\]
\[
-36 = 2 \times -18
\]

Now, our expression becomes:

\[
24x + 18y - 36 = 2(12x + 9y - 18)
\]

Thus, the final expression with 2 as a common factor is:

\[
2(12x + 9y - 18)
\]