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